Uniqueness and stability of solutions without the boundary condition

Abstract

Abstract A parabolic equation related to the p-Laplacian is considered. If the equation is degenerate on the boundary, then demonstrating the regularity on the boundary is difficult, the trace on the boundary cannot be defined, in general. The existence and uniqueness of weak solutions are researched. Based on uniqueness, the stability of solutions can be proved without any boundary condition.

Keywords

• p-Laplacian
• Existence
• Uniqueness
• Stability