Abstract
In this part we construct a unique bounded Hölder continuous viscosity solution for the nonlinear PDEs with the evolutionp-Laplacian equation and its anisotropic version as typical examples. The existence and properties of free boundaries will be discussed in part II.
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This research is supported by the National Natural Sciences Foundation of China.
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Zhan, Y. Viscosity solution theory of a class of nonlinear degenerate parabolic equations I. Uniqueness and existence of viscosity solutions. Acta Mathematicae Applicatae Sinica 13, 136–144 (1997). https://doi.org/10.1007/BF02015135
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DOI: https://doi.org/10.1007/BF02015135