Regularizing effect of absorption terms in singular and degenerate elliptic problems

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Main Authors: Sbai, Abdelaaziz, Hadfi, Youssef El
Format: Preprint
Published: 2020
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author Sbai, Abdelaaziz
Hadfi, Youssef El
author_facet Sbai, Abdelaaziz
Hadfi, Youssef El
contents In this paper we study the existence and regularity of solutions to the following singular problem \begin{equation} \left\{ \begin{array}{lll} &-\displaystyle\mbox{div} \big(a(x,u)|\nabla u|^{p-2}|\nabla u|\big) + |u|^{s-1}u =\frac{f}{u^γ} &\mbox{ in } Ω\\ &u>0 &\mbox{ in }Ω\\ &u=0 &\mbox{ on } δΩ\end{array} \right. \end{equation} proving that the lower order term $u|u|^{s-1}$ has some regularizing effects on the solutions in the case of an elliptic operator with degenerate coercivity.
format Preprint
id arxiv_https___arxiv_org_abs_2008_03597
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Regularizing effect of absorption terms in singular and degenerate elliptic problems
Sbai, Abdelaaziz
Hadfi, Youssef El
Analysis of PDEs
35A21, 35B20, 35B25, 35B45, 35D30, 35J60, 35J70, 35J75
In this paper we study the existence and regularity of solutions to the following singular problem \begin{equation} \left\{ \begin{array}{lll} &-\displaystyle\mbox{div} \big(a(x,u)|\nabla u|^{p-2}|\nabla u|\big) + |u|^{s-1}u =\frac{f}{u^γ} &\mbox{ in } Ω\\ &u>0 &\mbox{ in }Ω\\ &u=0 &\mbox{ on } δΩ\end{array} \right. \end{equation} proving that the lower order term $u|u|^{s-1}$ has some regularizing effects on the solutions in the case of an elliptic operator with degenerate coercivity.
title Regularizing effect of absorption terms in singular and degenerate elliptic problems
topic Analysis of PDEs
35A21, 35B20, 35B25, 35B45, 35D30, 35J60, 35J70, 35J75
url https://arxiv.org/abs/2008.03597