Existence for doubly nonlinear fractional $p$-Laplacian equations

Kenta Nakamura; Masashi Misawa; Nobuyuki Kato; Yoshihiko Yamaura

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

Existence for doubly nonlinear fractional p-Laplacian equations

Nobuyuki Kato , Masashi Misawa , Kenta Nakamura , Yoshihiko Yamaura This is my paper

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keywords doublyfractionalnonlinearexistencelaplacianweakcasesconvergence

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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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Existence for doubly nonlinear fractional p-Laplacian equations

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