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Abstract <p>We investigate an anisotropic elliptic equation of the second order with variable exponents in nonlinearities and a locally summable right-hand side in <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8404_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{R}^{n}\)</EquationSource> <!--LobJMat2560863Kozhevnikova-m3--> </InlineEquation>. In an anisotropic Sobolev space with variable exponents, the existence and regularity of a local renormalized solution is established, and it is proved that the solution is sign-constant.</p>

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Local Renormalized Solution of Anisotropic Elliptic Equation with Variable Exponents in Nonlinearities in \(\boldsymbol{\mathbb{R}^{n}}\)

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • L. M. Kozhevnikova

摘要

Abstract

We investigate an anisotropic elliptic equation of the second order with variable exponents in nonlinearities and a locally summable right-hand side in \(\mathbb{R}^{n}\) . In an anisotropic Sobolev space with variable exponents, the existence and regularity of a local renormalized solution is established, and it is proved that the solution is sign-constant.