The existence of strong solution for a class of fully nonlinear equation. (English) Zbl 1446.35005
Summary: 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.
MSC:
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35D35 | Strong solutions to PDEs |
| 35D30 | Weak solutions to PDEs |
| 35G30 | Boundary value problems for nonlinear higher-order PDEs |
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 47S99 | Other (nonclassical) types of operator theory |
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