English

Existence of Strong Solutions to Degenerate or Singular Strongly Coupled Elliptic Systems

Analysis of PDEs 2017-05-17 v1

Abstract

A general class of strongly coupled elliptic systems with quadratic growth in gradients is considered and the existence of their strong solutions is established. The results greatly improve those in a recent paper \cite{dleJFA} as the systems can be either degenerate or singular when their solutions become unbounded. A unified proof for both cases is presented. Most importantly, the VMO assumption in \cite{dleJFA} will be replaced by a much versatile one thanks to a new local weighted Gagliardo-Nirenberg involving BMO norms. Examples in physical models will be provided.

Keywords

Cite

@article{arxiv.1705.05490,
  title  = {Existence of Strong Solutions to Degenerate or Singular Strongly Coupled Elliptic Systems},
  author = {Dung Le},
  journal= {arXiv preprint arXiv:1705.05490},
  year   = {2017}
}