The boundary value condition of an evolutionary p ( x ) $p(x)$ -Laplacian equation

Huashui Zhan
2015 Boundary Value Problems  
Consider an evolutionary equation related to the p(x)-Laplacian: , the equation is degenerate on the boundary, one may expect that there is not flux across the boundary. The paper shows that the facts may be unexpected. The paper reviews Fichera-Oleinik theory, then uses the theory to discuss the boundary value condition related to the equation. If p -> 2, the existence and the uniqueness of the solutions are researched. Finally, if b i ≡ 0, the behavior of the solutions near the boundary is
more » ... the boundary is studied by the comparison theorem. MSC: 35L65; 35K85; 35R35
doi:10.1186/s13661-015-0377-6 fatcat:e4reme6z2rf4vafuyol5iz6g64