L2, Φ Regularity for Nonlinear Elliptic Systems of Second Order
Date
2002-02-19
Authors
Danecek, Josef
Viszus, Eugen
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
This paper is concerned with the regularity of the gradient of the weak solutions to nonlinear elliptic systems with linear main parts. It demonstrates the connection between the regularity of the (generally discontinuous) coefficients of the linear parts of systems and the regularity of the gradient of the weak solutions of systems. More precisely: If above-mentioned coefficients belong to the class L∞(Ω) ∩ L2,ψ(Ω) (generalized Campanato spaces), then the gradient of the weak solutions belong to L2,Φloc (Ω, ℝnN), where the relation between the functions ψ and Φ is formulated in Theorems 3.1 and 3.2 below.
Description
Keywords
Nonlinear equations, Regularity, Morrey-Campanato spaces
Citation
Danecek, J., & Viszus, E. (2002). L2, Φ Regularity for Nonlinear Elliptic Systems of Second Order. <i>Electronic Journal of Differential Equations, 2002</i>(20), pp. 1-13.
Rights
Attribution 4.0 International