Gradient regularity in mixed local and nonlocal problems

2022/04/13 by Cristiana De Filippis, Giuseppe Mingione, De Filippis, Cristiana +1 · 6 citations
Mathematics · #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2204.06590

openalex publication_date 2022/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Minimizers of functionals of mixed local and nonlocal type are locally C^1,β-regular.

Cited by

• Interior C^1,α regularity of mixed local-nonlocal (p,q)-energy minimizers for p≤ sq
• Mixed local-nonlocal equations with critical nonlinearity on ℝ^N: Non-existence, Existence, and Multiplicity of positive solutions
• Universal Potential Estimates for Mixed Local and Nonlocal Nonlinear Measure Data Problems
• Regularity theory for mixed local-nonlocal problem involving general stable operators
• Two alternative proofs of weak Harnack inequality for mixed local and nonlocal p-Laplace equations with a nonhomogeneity
• Regularity for Mixed Local and Nonlocal Degenerate Elliptic Equations in the Heisenberg Group

Related

• Global gradient regularity and a Hopf lemma for quasilinear operators of mixed local-nonlocal type
• Regularity results on a class of doubly nonlocal problems
• Regularity for nonlocal problems with non-standard growth
• Interior C^1,α regularity of mixed local-nonlocal (p,q)-energy minimizers for p≤ sq
• Riesz potential estimates for mixed local-nonlocal problems with measure data