تقرير
Lipschitz regularity for solutions of a general class of elliptic equations
| العنوان: | Lipschitz regularity for solutions of a general class of elliptic equations |
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| المؤلفون: | Marino, Greta, Mosconi, Sunra |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 30C65, 35B65, 35J60 |
| الوصف: | We prove local Lipschitz regularity for local minimiser of \[ W^{1,1}(\Omega)\ni v\mapsto \int_\Omega F(Dv)\, dx \] where $\Omega\subseteq {\mathbb R}^N$, $N\ge 2$ and $F:{\mathbb R}^N\to {\mathbb R}$ is a quasiuniformly convex integrand in the sense of Kovalev and Maldonado, i.e. a convex $C^1$-function such that the ratio between the maximum and minimum eigenvalues of $D^2F$ is essentially bounded. This class of integrands inculdes the standard singular/degenerate functions $F(z)=|z|^p$ for any $p>1$ and arises naturally as the closure, with respect to a natural convergence, of the strongly elliptic integrands of the Calculus of Variations. Comment: typo fixed in (1.5), 37 pages, comments welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2304.00657 |
| رقم الأكسشن: | edsarx.2304.00657 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |