Maximum principle for the fractional N-Laplacian flow

We deal with a family of the fractional N-Laplacian heat flows with variable exponent time-derivative on the Orlicz-Sobolev spaces. We get the maximum principle for these problems. We use the approximating method to get this result: We first show existence of a unique family of the approximating weak solutions from the variable exponent difference fractional N-Laplacian problems. We next show the maximum principle for the family of the approximating weak solution from the variable exponent difference fractional N-Laplacian problem, show the convergence of a family of the approximating weak solutions to the limits, and then obtain the maximum principle for the weak solution of a family of the fractional N-Laplacian heat flows with the variable exponent time-derivative on the Orlicz-Sobolev spaces.

Keywords

Fractional N-Laplacian heat flow, Difference fractional N-Laplacian operators, Young function, N-function, Orlicz space, Orlicz-Sobolev space, approximation method, approximating weak solution

2010 Mathematics Subject Classification

35A01, 35A25, 35B50, 35D30, 35K35, 46E30

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Received 23 February 2023

Published 21 May 2024