Hölder regularity of weak solutions to nonlocal p-Laplacian type Schrödinger equations with A₁^p-Muckenhoupt potentials

2023/06/01 by Yong‐Cheol Kim, Kim, Yong-Cheol
Mathematics · #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2306.00511

Abstract

In this paper, using the De Giorgi-Nash-Moser method, we obtain an interior Hölder continuity of weak solutions to nonlocal p-Laplacian type Schrödinger equations given by an integro-differential operator \rm L^p_K (p>1) as follows; \begincases \rm L^p_K u+V|u|^p-2 u=0 amp; in Ω, u=g amp;\text in \Bbb Rⁿ∖Ω \endcases where V=V₊-V_- with (V_-,V₊)∈ L¹_loc(\Bbb Rⁿ)× L^q_loc(\Bbb Rⁿ) for q>(n)/(ps)>1 and 0(n)/(ps)>1, 0

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• Regularity estimates for nonlocal Schrödinger equations
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