Regularizing Effect for a Nonlocal Maxwell-Schrödinger System

2025/07/16 by de Miranda, Luís Henrique, Santana, Ayana Pinheiro de Castro
#35B45 #35B65 #35D30 #35D99 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.12294

Abstract

In this paper we prove existence and regularity of weak solutions for the following system \begincases amp;-div((‖∇ u‖^p_L^p+‖∇ v‖^p_L^p)|∇ u|^p-2∇ u) + g(x,u,v)=f in Ω; amp;-div((‖∇ u‖^p_L^p+‖∇ v‖^p_L^p)|∇ v|^p-2∇ v) = h(x,u,v) in Ω; amp;u=v=0 on ∂Ω. \endcases where Ω is an open bounded subset of ℝ^N, N>2, f∈ L^m(Ω), where m>1 and g, h are two Carathéodory functions, which may be non monotone. We prove that under appropriate conditions on g and h, there is gain of Sobolev and Lebesgue regularity for the solutions of this system.

Citations

• Regularizing Effect for a Class of Maxwell-Schrödinger Systems

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