We establish the higher differentiability for the minimizers of the following non-autonomous integral functionals F(u,Ω)≔∫Ω∑i=1nai(x)|uxjavax.xml.bind.JAXBElement@6a9b708|pjavax.xml.bind.JAXBElement@31983172dx,with exponents pi≥2 and with coefficients ai(x) that satisfy a suitable Sobolev regularity. The main result is obtained, as usual, by imposing a gap bound on the exponents pi, which depends on the dimension and on the degree of regularity of the coefficients ai(x).
Higher differentiability of minimizers for non-autonomous orthotropic functionals / Russo, S.. - In: NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS. - ISSN 1468-1218. - 87:(2026). [10.1016/j.nonrwa.2025.104450]
Higher differentiability of minimizers for non-autonomous orthotropic functionals
Russo S.Primo
2026
Abstract
We establish the higher differentiability for the minimizers of the following non-autonomous integral functionals F(u,Ω)≔∫Ω∑i=1nai(x)|uxjavax.xml.bind.JAXBElement@6a9b708|pjavax.xml.bind.JAXBElement@31983172dx,with exponents pi≥2 and with coefficients ai(x) that satisfy a suitable Sobolev regularity. The main result is obtained, as usual, by imposing a gap bound on the exponents pi, which depends on the dimension and on the degree of regularity of the coefficients ai(x).| File | Dimensione | Formato | |
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