<abstract xmlns="http://www.w3.org/1999/xhtml">

Let Ω ⊂ ℝn<italic></italic> be an open set. We give a new characterization of zero trace functions <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2022-0020_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>f</mi><mo>∈</mo><mi>𝒞</mi><mrow><mo>(</mo><mover accent="true"><mi mathvariant="normal">Ω</mi><mo>¯</mo></mover><mo>)</mo></mrow><mo>∩</mo><msubsup><mrow><mi>W</mi></mrow><mn>0</mn><mrow><mn>1</mn><mo>,</mo><mi>p</mi><mrow><mo>(</mo><mo>.</mo><mo>)</mo></mrow></mrow></msubsup><mrow><mo>(</mo><mi mathvariant="normal">Ω</mi><mo>)</mo></mrow></mrow></math>
<tex-math>f \in \mathcal{C}\left( {\bar \Omega } \right) \cap W_0^{1,p\left( . \right)}\left( \Omega \right)</tex-math>
</alternatives>
</inline-formula>. If in addition Ω is bounded, then we give a sufficient condition for which the mapping <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2022-0020_eq_002.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>f</mi><mo>↦</mo><msubsup><mrow><mi>ℒ</mi></mrow><mrow><mi>p</mi><mrow><mo>(</mo><mo>.</mo><mo>)</mo></mrow><mo>,</mo><mi>f</mi></mrow><mi mathvariant="normal">Ω</mi></msubsup></mrow></math>
<tex-math>f \mapsto \mathcal{L}_{p\left( . \right),f}^\Omega</tex-math>
</alternatives>
</inline-formula> from a set of real extended functions <italic>f</italic> : <italic>∂</italic>Ω −→ ℝ to the nonlinear harmonic space (Ω,ℋℒ<italic>p</italic>(.)) is injective, where <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2022-0020_eq_003.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>ℒ</mi></mrow><mrow><mi>p</mi><mrow><mo>(</mo><mo>.</mo><mo>)</mo></mrow><mo>,</mo><mi>f</mi></mrow><mi mathvariant="normal">Ω</mi></msubsup></mrow></math>
<tex-math>\mathcal{L}_{p\left( . \right),f}^\Omega</tex-math>
</alternatives>
</inline-formula> denotes the Perron-Wiener-Brelot solution for the Dirichlet problem:
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2022-0020_eq_004.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mrow><mo>{</mo> <mrow><mtable columnalign="left"><mtr columnalign="left"><mtd columnalign="left"><mrow><msub><mrow><mi>ℒ</mi></mrow><mrow><mi>p</mi><mrow><mo>(</mo><mo>.</mo><mo>)</mo></mrow></mrow></msub><mi>u</mi><mo>:</mo><mo>=</mo><mo>-</mo><msub><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><mi>p</mi><mrow><mo>(</mo><mo>.</mo><mo>)</mo></mrow></mrow></msub><mi>u</mi><mo>+</mo><mi>ℬ</mi><mrow><mo>(</mo><mrow><mo>.</mo><mo>,</mo><mi>u</mi></mrow><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></mtd><mtd columnalign="left"><mrow><mi>i</mi><mi>n</mi><mi> </mi><mi mathvariant="normal">Ω</mi><mo>;</mo></mrow></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mrow><mi>u</mi><mo>=</mo><mi>f</mi></mrow></mtd><mtd columnalign="left"><mrow><mi>o</mi><mi>n</mi><mi> </mi><mo>∂</mo><mi mathvariant="normal">Ω</mi><mo>,</mo></mrow></mtd></mtr></mtable></mrow> </mrow></mrow></math>
<tex-math>\left\{ {\matrix{{{\mathcal{L}_{p\left( . \right)}}u: = - {\Delta _{p\left( . \right)}}u + \mathcal{B}\left( {.,u} \right) = 0} \hfill &amp; {in\,\Omega ;} \hfill \cr {u = f} \hfill &amp; {on\,\partial \Omega ,} \hfill \cr } } \right.</tex-math>
</alternatives>
</disp-formula>
where ℬ is a given Carathéodory function satisfies some structural conditions.
</abstract>

Capacitary characterization of variable exponent Sobolev trace spaces

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this work we extend the concept of (<italic>r</italic>; <italic>t</italic>; <italic>s</italic>)-nuclear operators presented by Lapresté in (Studia math., T. LVII. 1976, 47 – 83) to <italic>n</italic>-homogeneous polynomials. Factorization and inclusion properties are described. Under some conditions, we also characterize the topological dual of the studied space.
</abstract>

Laboratory of Pure and Applied Mathematics (LPAM)

On (<italic>r</italic>; <italic>t</italic>; <italic>s</italic>)-nuclear polynomials

<abstract xmlns="http://www.w3.org/1999/xhtml">

We study the existence and regularity results for non-linear elliptic equation with degenerate coercivity and a singular gradient lower order term. The model problems is
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2022-0022_eq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mrow><mo>{</mo> <mrow><mtable columnalign="left"><mtr columnalign="left"><mtd columnalign="left"><mrow><mo>-</mo><mi>d</mi><mi>i</mi><mi>v</mi><mrow><mo>(</mo><mrow><mi>b</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mfrac><mrow><msup><mrow><mrow><mrow><mo>|</mo> <mrow><mo>∇</mo><mi>u</mi></mrow> <mo>|</mo></mrow></mrow></mrow><mrow><mi>p</mi><mo>-</mo><mn>2</mn></mrow></msup><mo>∇</mo><mi>u</mi></mrow><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>+</mo><mrow><mo>|</mo> <mi>u</mi> <mo>|</mo></mrow></mrow><mo>)</mo></mrow><mi>γ</mi></mrow></mfrac></mrow><mo>)</mo></mrow><mo>+</mo><mfrac><mrow><msup><mrow><mrow><mrow><mo>|</mo> <mrow><mo>∇</mo><mi>u</mi></mrow> <mo>|</mo></mrow></mrow></mrow><mi>p</mi></msup></mrow><mrow><msup><mrow><mrow><mrow><mo>|</mo> <mi>u</mi> <mo>|</mo></mrow></mrow></mrow><mi>θ</mi></msup></mrow></mfrac><mo>=</mo><mi>f</mi><mo>,</mo></mrow></mtd><mtd columnalign="left"><mrow><mi>i</mi><mi>n</mi><mi> </mi><mi mathvariant="normal">Ω</mi><mo>,</mo></mrow></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mrow><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo></mrow></mtd><mtd columnalign="left"><mrow><mi>o</mi><mi>n</mi><mi> </mi><mo>∂</mo><mi mathvariant="normal">Ω</mi><mo>,</mo></mrow></mtd></mtr></mtable></mrow> </mrow></mrow></math>
<tex-math>\left\{ {\matrix{ { - div\left( {b\left( x \right){{{{\left| {\nabla u} \right|}^{p - 2}}\nabla u} \over {\left( {1 + \left| u \right|} \right)\gamma }}} \right) + {{{{\left| {\nabla u} \right|}^p}} \over {{{\left| u \right|}^\theta }}} = f,} \hfill &amp; {in\,\Omega ,} \hfill \cr {u = 0,} \hfill &amp; {on\,\partial \Omega ,} \hfill \cr } } \right.</tex-math>
</alternatives>
</disp-formula> swhere Ω is a bounded open subset in ℝN, 1 ≤ <italic>θ</italic> &lt; 2, <italic>p</italic> > 2 and <italic>γ</italic> > 0. We will show that, even if the lower order term is singular, we obtain existence and regularity of positive solution, under various assumptions on the summability of the source <italic>f</italic>.
</abstract>

Existence and Regularity for Solution to a Degenerate Problem with Singular Gradient Lower Order Term

<abstract xmlns="http://www.w3.org/1999/xhtml">

This work is devoted to the study of a new class of parabolic problems in inhomogeneous Orlicz spaces with gradient constraints and <italic>L</italic>1-data. One proves the existence of the solution by studying the asymptotic behaviour as <italic>p</italic> goes to ∞, of a sequence of entropy solutions (<italic>up</italic>) of some nonlinear parabolic equation in inhomogeneous Orlicz-Sobolev spaces with <italic>L</italic>1-data involving the parameter <italic>p</italic>.
</abstract>

Parabolic inequalities in inhomogeneous Orlicz-Sobolev spaces with gradients constraints and <italic>L</italic>1-data

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we investigate the limit points set of descent spectrum of upper triangular operator matrices <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2022-0024_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>M</mi></mrow><mi>C</mi></msub><mo>=</mo><mrow><mo>(</mo><mrow><mtable columnalign="left"><mtr columnalign="left"><mtd columnalign="left"><mi>A</mi></mtd><mtd columnalign="left"><mi>C</mi></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mn>0</mn></mtd><mtd columnalign="left"><mi>B</mi></mtd></mtr></mtable></mrow><mo>)</mo></mrow></mrow></math>
<tex-math>{M_C} = \left( {\matrix{A \hfill &amp; C \hfill \cr 0 \hfill &amp; B \hfill \cr } } \right)</tex-math>
</alternatives>
</inline-formula>. We prove that <italic>acc</italic>(<italic>σdes</italic>(<italic>MC</italic>)) ∪ <italic>Waccσdes</italic> = <italic>acc</italic>(<italic>σdes</italic>(<italic>A</italic>)) ∪ <italic>acc</italic>(<italic>σdes</italic>(<italic>B</italic>)) where <italic>Waccσdes</italic> is the union of certain holes in <italic>acc</italic>(<italic>σdes</italic>(<italic>MC</italic>)), which happen to be subsets of <italic>acc</italic>(<italic>σasc</italic>(<italic>B</italic>)) ∩ <italic>acc</italic>(<italic>σdes</italic>(<italic>A</italic>)). Furthermore, several sufficient conditions for <italic>acc</italic>(<italic>σdes</italic>(<italic>MC</italic>)) = <italic>acc</italic>(<italic>σdes</italic>(<italic>A</italic>)) ∪ <italic>acc</italic>(<italic>σdes</italic>(<italic>B</italic>)) holds for every <italic>C</italic> ∈ ℬ(<italic>Y</italic>, <italic>X</italic>) are given.
</abstract>

Limit points for descent spectrum of operator matrices

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we introduce a new family of stochastic Lundqvist-Korf diffusion process, defined from a <italic>g</italic>-power of the Lundqvist-Korf diffusion process. First, we determine the probabilistic characteristics of the process, such as its analytic expression, the transition probability density function from the corresponding It ˆo stochastic differential equation and obtain the conditional and non-conditional mean functions. We then study the statistical inference in this process. The parameters of this process are estimated by using the maximum likelihood estimation method with discrete sampling, thus we obtain a nonlinear equation, which is achieved via the simulated annealing algorithm. Finally, the results of the paper are applied to simulated data.
</abstract>

Department of Mathematics and Computer Science

Laboratory of Systems Modelization and Analysis for Decision Support

A <italic>γ</italic>-power stochastic Lundqvist-Korf diffusion process: Computational aspects and simulation

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper we study a model of full Von-Karman system coupled to the thermoelastic equations, with rotational forces, nor clamped boundary conditions. Our fundamental goal is to establish the existence as well as the uniqueness of a weak solution for the so-called global energy. As the end we displays a numerical simulation.
</abstract>

Existence, uniqueness weak solution for a dynamic Full von Karman System of thermoelasticity

<abstract xmlns="http://www.w3.org/1999/xhtml">

We analyze a finite volume scheme for a nonlinear reaction-diffusion system applied to image processing. First, we demonstrate the existence of a solution to the finite volume scheme. Then, based on the derivation of a series of a priori estimates and the use of Kolmogorov’s compactness criterion, we prove that the solution to the finite volume scheme converges to the weak solution. In the numerical experiments, we show the effectiveness of the proposed model with respect to the modified (in the sense of Catté, Lions, Morel and Coll) Perona-Malik nonlinear image selective smoothing equation in terms of preserving small details, texture, and fine structures.
</abstract>

Convergence of a finite volume scheme for a parabolic system applied to image processing

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Moroccan Journal of Pure and Applied Analysis

 The Moroccan Journal of Pure and Applied Analysis "MJPAA" (Print ISSN: 2605-6364) is a peer-reviewed open access journal published by the "Université Sidi Mohamed Ben Abdellah" (Sidi Mohamed Ben Abdallah University), covering all main-stream branches of pure and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, numerical analysis, optimization theory, and control theory.   MJPAA is published by Sidi Mohamed Ben Abdallah University in three issues in January, May and September.   Why subscribe and read    The journal covers a wide range of branches of mathematical analysis.   Pure and applied analysis topics are intensely studied by researchers throughout the world especially in Africa, the Arab and European countries.   An edition committee of high-level and international renown.   Editorial board representing different regions of the world and various research teams.      Why submit    No publication charges for the authors or their institutions.   The journal is available to be indexed in the most important databases.   The journal is among the best in its field in Africa and the Arab world.      Rejection Rate    45%      Archiving   Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.   Plagiarism Policy   The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process.   Publisher:Sidi Mohamed Ben Abdallah University (Route Imouzzer, BP 2626 Fez 30000, Morocco, Tel. : 0212 5 35 60 96 60/ 61)   Contact:Professor Youssef Akdim, Sidi Mohamed Ben Abdellah Universitymjpaa.edition1@usmba.ac.ma 

Moroccan Journal of Pure and Applied Analysis

Volume 8 (2022): Issue 3 (September 2022)

Capacitary characterization of variable exponent Sobolev trace spaces

On (r; t; s)-nuclear polynomials

Existence and Regularity for Solution to a Degenerate Problem with Singular Gradient Lower Order Term

Parabolic inequalities in inhomogeneous Orlicz-Sobolev spaces with gradients constraints and L¹-data

Limit points for descent spectrum of operator matrices

A γ-power stochastic Lundqvist-Korf diffusion process: Computational aspects and simulation

Existence, uniqueness weak solution for a dynamic Full von Karman System of thermoelasticity

Convergence of a finite volume scheme for a parabolic system applied to image processing

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