Local and global boundedness for some nonlinear parabolic equations exhibiting a time singularity.
In this paper the Authors consider doubly nonlinear operators in measure spaces equipped with a doubling non-trivial Borel measure supporting a weak Poincaré inequality. They prove local and global boundness of non-negative weak solutions giving a complete and definitive answer to this problem. The result is based on suitable energy estimates and depends on the dimension of the Borel measure.
scientific article; zbMATH DE number 6674872