<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we give a priori estimates near the boundary for solutions of a degenerate elliptic problems in the general Besov-type spaces <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2017-0013_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>B</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>τ</mi></mrow></msubsup></mrow></math><tex-math>$B_{p,q}^{s,\tau }$</tex-math></alternatives></inline-formula>, containing as special cases: Goldberg space <italic>bmo</italic>, local Morrey-Campanato spaces <italic>l</italic><sup>2</sup>,<italic>λ</italic> and the classical Hölder and Besov spaces <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2017-0013_eq_002.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>B</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow><mi>s</mi></msubsup></mrow></math><tex-math>$B_{p,q}^s $</tex-math></alternatives></inline-formula>. This work extends the results of [<xref ref-type="bibr" rid="j_mjpaa-2017-0013_ref_013_w2aab3b7b3b1b6b1ab1ac13Aa">13</xref>, <xref ref-type="bibr" rid="j_mjpaa-2017-0013_ref_002_w2aab3b7b3b1b6b1ab1ab2Aa">2</xref>, <xref ref-type="bibr" rid="j_mjpaa-2017-0013_ref_015_w2aab3b7b3b1b6b1ab1ac15Aa">15</xref>] from Hölder and Besov spaces to the general frame of <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2017-0013_eq_003.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>B</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>τ</mi></mrow></msubsup></mrow></math><tex-math>$B_{p,q}^{s,\tau }$</tex-math></alternatives></inline-formula> spaces.</p></abstract>

In this paper, we give a priori estimates near the boundary for solutions of a degenerate elliptic problems in the general Besov-type spaces Bp,qs,τ$B_{p,q}^{s,\tau }$, containing as special cases: Goldberg space bmo, local Morrey-Campanato spaces l2,λ and the classical Hölder and Besov spaces Bp,qs$B_{p,q}^s $. This work extends the results of [13, 2, 15] from Hölder and Besov spaces to the general frame of Bp,qs,τ$B_{p,q}^{s,\tau }$ spaces.

A-priori Estimates Near the Boundary for Solutions of a class of Degenerate Elliptic Problems in Besov-type Spaces

Moroccan Journal of Pure and Applied Analysis

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

In this paper, we give a priori estimates near the boundary for solutions of a degenerate elliptic problems in the general Besov-type spaces...

A-priori Estimates Near the Boundary for Solutions of a class of Degenerate Elliptic Problems in Besov-type Spaces

Publié en ligne: 28 juil. 2018

Pages: 149 - 172

Reçu: 13 mars 2018

Accepté: 06 juin 2018

DOI: https://doi.org/10.1515/mjpaa-2017-0013

Mots clés
A-priori estimates, degenerate elliptic equations, Besov-type spaces

© 2018 Azzeddine El Baraka et al., published by Sciendo

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

A-priori Estimates Near the Boundary for Solutions of a class of Degenerate Elliptic Problems in Besov-type Spaces

Publié en ligne: 28 juil. 2018

Pages: 149 - 172

Reçu: 13 mars 2018

Accepté: 06 juin 2018

DOI: https://doi.org/10.1515/mjpaa-2017-0013

Mots clésA-priori estimates, degenerate elliptic equations, Besov-type spaces

© 2018 Azzeddine El Baraka et al., published by Sciendo

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

Mots clés
A-priori estimates, degenerate elliptic equations, Besov-type spaces