Existence for doubly nonlinear fractional p-Laplacian equations

2023/05/01 by Nobuyuki Kato, Kato, Nobuyuki, Masashi Misawa +5 · 2 citations
Computer Science · Mathematics · #35B65 #35K61 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Primary: 35B45 #\quad Secondary: 35D30

paper · pdf · doi:10.48550/arxiv.2305.00661

openalex publication_date 2023/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Global well-posedness for a time-fractional doubly nonlinear equation
• Doubly nonlinear parabolic equation involving a mixed local-nonlocal operator and a convection term

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