Gradient regularity for double-phase orthotropic functionals

2025/07/24 by Almi, Stefano, Leone, Chiara, Manzo, Gianluigi
#35B65 #35J70 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.18474

Abstract

We prove higher integrability for local minimizers of the double-phase orthotropic functional ∑_i=1ⁿ∫_Ω(|u_xi|^p+a(x)| u_xi|^q)dx when the weight function a ≥0 is assumed to be α-Hölder continuous, while the exponents p, q are such that 2 ≤ p ≤ q and (q)/(p) < 1 + \fracαn. Under natural Sobolev regularity of~a, we further obtain explicit Lipschitz regularity estimates for local minimizers.

Citations

• Higher Differentiability of Minimizers for Non-Autonomous Orthotropic Functionals
• Singular orthotropic functionals with nonstandard growth conditions
• Absence of Lavrentiev's gap for anisotropic functionals
• Lipschitz regularity for orthotropic functionals with nonstandard growth conditions
• Regularity of the derivatives of p-orthotropic functions in the plane for 1
• Regularity for an anisotropic equation in the plane
• On the Lipschitz character of orthotropic p-harmonic functions
• Regularity for general functionals with double phase
• Regularity for general functionals with double phase
• Sobolev and Lipschitz regularity for local minimizers of widely\n degenerate anisotropic functionals
• Lipschitz regularity for local minimizers of some widely degenerate problems

Related

• Regularity for minimizers of degenerate, non-autonomous, orthotropic integral functionals
• Regularity results for mixed local and nonlocal double phase functionals
• Smoothness of weight sharply discards Lavrentiev's gap for double phase functionals
• Higher Differentiability of Minimizers for Non-Autonomous Orthotropic Functionals
• Lipschitz regularity for orthotropic functionals with nonstandard growth conditions