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arXiv · 1912.09541

$L^\infty$-bounds for general singular elliptic equations with convection term

Greta Marino·Patrick Winkert
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Abstract

In this note we present $L^\infty$-results for problems of the form $A(x,u,Du)=B(x,u,Du)$ in $\Omega$, $u>0$ in $\Omega$, $u=0$ on $\partial\Omega$, where the growth condition for the function $B\colon \Omega \times \mathbb{R}\times \mathbb{R}^N\to \mathbb{R}$ contains both a singular and a convection term. We use ideas from the works of Giacomoni-Schindler-Takac (2007) and the authors (2019) to prove the boundedness of weak solutions for such general problem by applying appropriate bootstrap arguments.

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Greta Marino, Patrick Winkert. 2019-12-19. $L^\infty$-bounds for general singular elliptic equations with convection term. https://arxiv.org/abs/1912.09541

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