Large-time geometric properties of solutions of the evolution \(p\)-Laplacian equation
The Cauchy problem for the parabolic \(p\)-Laplacian equation is considered. The authors prove a nonlinear concavity estimate for the pressure away from the maximum point provided the initial data are nonnegative, continuous and compactly supported. This estimate implies (among other things) the convexity of the support for large time.
scientific article; zbMATH DE number 5072893
scientific article