<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we are interested in the existence of solutions for Dirichlet problem associated with the degenerate nonlinear elliptic equations<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2019-0012_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><mo>-</mo><mtext>div</mtext><mrow><mo>[</mo><mrow><mi>𝒜</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mo>∇</mo><mi>u</mi></mrow><mo>)</mo></mrow><msub><mrow><mi>ω</mi></mrow><mn>1</mn></msub><mo>+</mo><mi>𝒝</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mo>∇</mo><mi>u</mi></mrow><mo>)</mo></mrow><msub><mrow><mi>ω</mi></mrow><mn>2</mn></msub></mrow><mo>]</mo></mrow><mo>=</mo><msub><mrow><mi>f</mi></mrow><mn>0</mn></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>-</mo><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow><msub><mrow><mi>D</mi></mrow><mi>j</mi></msub><msub><mrow><mi>f</mi></mrow><mi>j</mi></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi> </mi><mi> </mi><mtext>in</mtext></mrow><mi> </mi><mi> </mi><mi> </mi><mi> </mi><mi> </mi><mi>Ω</mi><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn><mi> </mi><mi> </mi><mi> </mi><mi> </mi><mtext>on</mtext><mi> </mi><mi> </mi><mi> </mi><mi> </mi><mo>∂</mo><mi>Ω</mi><mo>,</mo></mrow></mtd></mtr></mtable></mrow></mrow></mrow></math><tex-math>\left\{ {\matrix{ { - {\rm{div}}\left[ {\mathcal{A}\left( {x,\nabla u} \right){\omega _1} + \mathcal{B}\left( {x,u,\nabla u} \right){\omega _2}} \right] = {f_0}\left( x \right) - \sum\limits_{j = 1}^n {{D_j}{f_j}\left( x \right)\,\,{\rm{in}}} \,\,\,\,\,\Omega ,} \hfill \cr {u\left( x \right) = 0\,\,\,\,{\rm{on}}\,\,\,\,\partial \Omega {\rm{,}}} \hfill \cr } } \right.</tex-math></alternatives></disp-formula>in the setting of the weighted Sobolev spaces.</abstract>

In this paper we are interested in the existence of solutions for Dirichlet problem associated with the degenerate nonlinear elliptic equations{-div[𝒜(x,∇u)ω1+𝒝(x,u,∇u)ω2]=f0(x)-∑j=1nDjfj(x)  in     Ω,u(x)=0    on    ∂Ω,\left\{ {\matrix{ { - {\rm{div}}\left[ {\mathcal{A}\left( {x,\nabla u} \right){\omega _1} + \mathcal{B}\left( {x,u,\nabla u} \right){\omega _2}} \right] = {f_0}\left( x \right) - \sum\limits_{j = 1}^n {{D_j}{f_j}\left( x \right)\,\,{\rm{in}}} \,\,\,\,\,\Omega ,} \hfill \cr {u\left( x \right) = 0\,\,\,\,{\rm{on}}\,\,\,\,\partial \Omega {\rm{,}}} \hfill \cr } } \right.in the setting of the weighted Sobolev spaces.

Existence Results For A Class Of Nonlinear Degenerate Elliptic Equations

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Existence Results For A Class Of Nonlinear Degenerate Elliptic Equations"}

In this paper we are interested in the existence of solutions for Dirichlet problem associated with the degenerate nonlinear elliptic...

Existence Results For A Class Of Nonlinear Degenerate Elliptic Equations

Publié en ligne: 24 janv. 2020

Pages: 164 - 178

Reçu: 17 sept. 2019

Accepté: 04 nov. 2019

DOI: https://doi.org/10.2478/mjpaa-2019-0012

Mots clés
Degenerate Nonlinear Elliptic Equations, Weighted Sobolev Spaces

© 2019 Albo Carlos Cavalheiro, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Existence Results For A Class Of Nonlinear Degenerate Elliptic Equations

Publié en ligne: 24 janv. 2020

Pages: 164 - 178

Reçu: 17 sept. 2019

Accepté: 04 nov. 2019

DOI: https://doi.org/10.2478/mjpaa-2019-0012

Mots clésDegenerate Nonlinear Elliptic Equations, Weighted Sobolev Spaces

© 2019 Albo Carlos Cavalheiro, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
Degenerate Nonlinear Elliptic Equations, Weighted Sobolev Spaces