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arXiv · 2412.07540

Bounded solutions of degenerate elliptic equations with an Orlicz-gain Sobolev inequality

David Cruz-Uribe·Sullivan F. MacDonald·Scott Rodney
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Abstract

We consider the boundedness and exponential integrability of solutions to the Dirichlet problem for the degenerate elliptic equation \[ -v^{-1}\mathrm{Div}(|\sqrt{Q}\nabla u|^{p-2}Q\nabla u)=f|f|^{p-2}- v^{-1}\mathrm{Div}(v|g|^{p-2}g \mathbf{t}), \quad 1 1$. In our results we study the interplay between the Sobolev inequality and the regularity assumptions needed on $f$ and $g$ to prove that the solution is bounded or is exponentially integrable. Our results generalize those previously proved in previous work by the authors.

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David Cruz-Uribe, Sullivan F. MacDonald, Scott Rodney. 2024-12-10. Bounded solutions of degenerate elliptic equations with an Orlicz-gain Sobolev inequality. https://arxiv.org/abs/2412.07540

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