Global C1,α regularity for variable exponent elliptic equations in divergence form

2007

377 citations recorded by the source corpus.

Abstract We study the global C 1 , α regularity of the bounded generalized solutions of the variable exponent elliptic equations in divergence form with both Dirichlet and Neumann boundary conditions. Our results are a generalization of the corresponding results in the constant exponent case.

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

View Paper: https://www.semanticscholar.org/paper/5f015d161bbe86b576e4c07fe22284957b65068c

Citations in the corpus

• Local-to-global results in variable exponent spaces (2009, neutral): “[3, 4, 6, 17, 19, 22, 24, 31, 39].”
• Overview of differential equations with non-standard growth (2010, methodology): “[86] Fan, X.”
• MAXIMAL FUNCTIONS IN VARIABLE EXPONENT SPACES: LIMITING CASES OF THE EXPONENT (2009, background): “[7, 12, 17, 29, 31], with related differential equations [1, 3, 15, 16, 32, 41, 42], and with applications [4, 38].”
• Triebel-Lizorkin-Type Spaces with Variable Exponents (2015, background): “, [6, 12, 13, 14, 17, 18, 19, 21, 32, 48]. The motivation to study such function spaces also comes from applications to fluid dynamic, image processing and the calculus of variation; see, for example, [1, 2, 3, 11, 21, 25, 59, 60]. To complete the theory of the variable exponent Lebesgue and Sobolev ”
• Function spaces of variable smoothness and integrability (2007, background): “Apart from interesting theor tical considerations, the motivation to study such function spaces comes from applications to fluid dynamics, image processing, PDE and the calculus of variation.”
• Existence of Positive Solutions for p(x)-Laplacian Equations with a Singular Nonlinear Term (2014, background): “For example, the regularity of weak solutions for differential equations with variable exponent was studied in [1, 7], and existence of solutions for variable exponent problems was studied in a series of papers [3, 9, 12, 20, 24, 30, 33, 36, 39, 44, 45].”
• Besov-Type Spaces with Variable Smoothness and Integrability (2015, background): “Apart from theoretical considerations, such function spaces have interesting applications in fluid dynamics [1, 57], image processing [7], partial differential equations and variational calculus [2, 20, 25, 54, 58].”
• Besov spaces with variable smoothness and integrability (2010, background): “Apart from interesting theoretical considerations, the motivation to study such function spaces comes from applications to fluid dynamics [1, 2, 34], image processing [11], PDE and the calculus of variation [3, 16, 18, 20, 28, 35, 47].”
• Gradient estimates for elliptic equations with Lp(·)logL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{p(\cdot )}\ (2016, background): “For regularity results of the minimizers of functionals or weak solutions to equations associated with the Orlicz class and the variable exponent class, we refer to [4,12,15,18,19,27,33] and [1,2,5,10,16,17,34], respectively, and references therein.”