The Dirichlet problem for possibly singular elliptic equations with degenerate coercivity

We deal with existence, uniqueness and regularity of nonnegative solutions to a Dirichlet problem for equations as \begin{equation*} \displaystyle -\operatorname{div}\left(\frac{|\nabla u|^{p-2}\nabla u}{(1+u)^{\theta(p-1)}}\right) = h(u)f \quad \text{in }\Omega, \end{equation*} where \(\Omega\) is...

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Bibliographic Details
Published in:arXiv.org 2023-06
Main Authors: Durastanti, Riccardo, Oliva, Francescantonio
Format: Article
Language:English
Subjects:
Coercivity
Continuity (mathematics)
Dirichlet problem
Elliptic functions
Mathematical analysis
Online Access:Get full text
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Summary:We deal with existence, uniqueness and regularity of nonnegative solutions to a Dirichlet problem for equations as \begin{equation*} \displaystyle -\operatorname{div}\left(\frac{|\nabla u|^{p-2}\nabla u}{(1+u)^{\theta(p-1)}}\right) = h(u)f \quad \text{in }\Omega, \end{equation*} where \(\Omega\) is an open bounded subset of \(\mathbb{R}^N\) (\(N\ge 2\)), \(p>1\), \(\theta\ge 0\), \(f\geq 0\) belongs to a suitable Lebesgue space and \(h\) is a continuous, nonnegative function which may blow up at zero and it is bounded at infinity.
ISSN:2331-8422
DOI:10.48550/arxiv.2105.13453