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Existence for doubly nonlinear fractional $p$-Laplacian equations

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arxiv 2305.00661 v1 pith:2A2BRSMZ submitted 2023-05-01 math.AP

Nobuyuki Kato , Masashi Misawa , Kenta Nakamura , Yoshihiko Yamaura This is my paper · ORCID
classification math.AP
keywords doublyfractionalnonlinearexistencelaplacianweakcasesconvergence
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abstract

In this paper we prove the existence of a weak solution to a doubly nonlinear parabolic fractional $p$-Laplacian equation, which has general doubly non-linearlity including not only the Sobolev subcritical/critical/supercritical cases but also the slow/fast diffusion ones. Our proof reveals the weak convergence method for the doubly nonlinear fractional $p$-Laplace operator.

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