Lipschitz regularity for degenerate elliptic integrals with p,q-growth

2021/01/04 by Giovanni Cupini, Paolo Marcellini, Cupini, Giovanni +5 · 2 citations
Computer Science · Mathematics · #35J50 #49N60 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2101.01101

openalex publication_date 2021/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We establish the local Lipschitz continuity and the higher differentiability of vector-valued local minimizers of a class of energy integrals of the Calculus of Variations. The main novelty is that we deal with possibly degenerate energy densities with respect to the x-variable.

Cited by

• Global boundedness of weak solutions with finite energy to a general class of Dirichlet problems
• Local Lipschitz continuity for energy integrals with fast growth and lower order terms

Related

• Unified a-priori estimates for minimizers under p,q-growth and exponential growth
• Lipschitz regularity for a priori bounded minimizers of integral functionals with nonstandard growth
• Local Lipschitz continuity for energy integrals with slow growth
• Lipschitz bounds for integral functionals with (p,q)-growth conditions
• Local Lipschitz continuity for energy integrals with fast growth and lower order terms