{"title":"Higher differentiability of minimizers for non-autonomous orthotropic functionals","authors":"Stefania Russo","doi":"10.1016/j.nonrwa.2025.104450","DOIUrl":null,"url":null,"abstract":"<div><div>We establish the higher differentiability for the minimizers of the following non-autonomous integral functionals <span><span><span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>Ω</mi><mo>)</mo></mrow><mo>≔</mo><mspace></mspace><msub><mrow><mo>∫</mo></mrow><mrow><mi>Ω</mi></mrow></msub><munderover><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></munderover><mspace></mspace><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mrow><mrow><mo>|</mo><msub><mrow><mi>u</mi></mrow><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>|</mo></mrow></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msup><mi>d</mi><mi>x</mi><mo>,</mo></mrow></math></span></span></span>with exponents <span><math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>≥</mo><mn>2</mn></mrow></math></span> and with coefficients <span><math><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> that satisfy a suitable Sobolev regularity. The main result is obtained, as usual, by imposing a gap bound on the exponents <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>, which depends on the dimension and on the degree of regularity of the coefficients <span><math><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span>.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104450"},"PeriodicalIF":1.8000,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121825001361","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We establish the higher differentiability for the minimizers of the following non-autonomous integral functionals with exponents and with coefficients that satisfy a suitable Sobolev regularity. The main result is obtained, as usual, by imposing a gap bound on the exponents , which depends on the dimension and on the degree of regularity of the coefficients .
期刊介绍:
Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems.
The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.