某些双相问题的正则化效应

IF 1.4 4区工程技术 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Mathematics in Engineering Pub Date : 2022-01-01 DOI:10.3934/mine.2023069

L. Boccardo, G. R. Cirmi

引用次数: 0

摘要

In this paper we study the existence of solutions of the Dirichlet problem associated to the following nonlinear PDE \begin{document}$ \begin{equation*} { } -{{{\rm{\;div}}}}\big(a(x)\,\nabla u|\nabla u|^{p-2}\big) -{{{\rm{\;div}}}}\big( |u|^{(r-1)\lambda+1}\nabla u|\nabla u|^{\lambda-2}\big) = f \end{equation*} $\end{document} where $ 1 < \lambda \leq p $, $ r > 1 $ and $ f \in L^1(\Omega) $.

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Regularizing effect in some double phase problems

In this paper we study the existence of solutions of the Dirichlet problem associated to the following nonlinear PDE

\begin{document}$ \begin{equation*} { } -{{{\rm{\;div}}}}\big(a(x)\,\nabla u|\nabla u|^{p-2}\big) -{{{\rm{\;div}}}}\big( |u|^{(r-1)\lambda+1}\nabla u|\nabla u|^{\lambda-2}\big) = f \end{equation*} $\end{document}

where $ 1 < \lambda \leq p $, $ r > 1 $ and $ f \in L^1(\Omega) $.

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