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arXiv · 2403.11315

On widely degenerate \textit{p}-Laplace equations with symmetric data

Stefania Russo
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Abstract

In this paper, we consider the Dirichlet problems with a widely degenerate equation. Through a well-known result by Talenti, we explicitly express the gradient of the solution $u_p$ outside the ball with a radius of $1$, if the datum $f$ is a non-negative radially decreasing function. This allows us to establish some sharp higher regularity results for the weak solutions, assuming that the datum $f$ belongs to a suitable Lorentz space, i.e. under a weaker assumption on the datum with respect to the available literature. Moreover we analyze the behaviour of $u_p$ as $p \to 1^+$.

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Stefania Russo. 2024-03-17. On widely degenerate \textit{p}-Laplace equations with symmetric data. https://arxiv.org/abs/2403.11315

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