The existence of strong solution for a class of fully nonlinear equation

Abstract

This article mainly investigates the existence of global strong solution of a class of fully nonlinear evolution equation and the strong solution of its steady-state equation. By using the T-compulsorily weakly continuous operator theory, the existence of the global strong solution of the fully nonlinear evolution equation is obtained. In addition, based on the acute angle principle, the W 2,p -strong solution for the corresponding stationary equation is also derived. KEYWORDS acute angle principle, fully nonlinear equation, strong solution, T-compulsorily weakly continuous operator theory MSC CLASSIFICATION 35A01; 35D35; 35D30; 47S99 Math Meth Appl Sci. 2020;43:1530-1542. wileyonlinelibrary.com/journal/mma