Regularity for Double Phase Problems at Nearly Linear Growth

By Cristiana De Filippis, Giuseppe Mingione. Archive for Rational Mechanics and Analysis, 2023

76 citations recorded by the source corpus.

Minima of functionals of the type w↦∫Ω|Dw|log(1+|Dw|)+a(x)|Dw|qdx,0≤a(·)∈C0,α,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} w\mapsto \int _{\varOmega }\left[ |Dw|\log (1+|Dw|)+a(x)|Dw|^{q}\right] \, \textrm{d}x, \quad 0\le a(\cdot ) \in C^{0, \alpha }, \end{aligned}$$\end{document}with Ω⊂Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varOmega \subset {\mathbb {R}}^n$$\end{document}, have locally Hölder continuous gradient provided 1<q<1+α/n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1< q < 1+\alpha /n$$\end{document}.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0c606f8aa46926fea55d2b9c1fcf733c6f52c430