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This is a Quantitative Study study.

October 15, 2025Open Access

Regularizing Effect for a Nonlocal Maxwell-Schrödinger System

Key Points

Weak solutions exist for a nonlocal maxwell-schrödinger system, improving understanding of mathematical behavior.
The system demonstrates regularity gains under specific conditions related to carathéodory functions.
Conditions are explored where sobolev and lebesgue regularity improve, showing potential for broader applications.
Analysis is conducted in an open bounded subset of real numbers, with significant implications for theoretical models.

Abstract

In this paper we prove existence and regularity of weak solutions for the following system align* cases &u=v=0 \ on \ Ω. cases align* where Ω is an open bounded subset of RN, N>2, f Lᵐ (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.

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Cite This Study

Miranda et al. (Wed,) studied this question.

synapsesocial.com/papers/68ef858cc6a308ba0635576d https://doi.org/https://doi.org/10.48550/arxiv.2507.12294