Regularity results for quasiminima of a class of double phase problems

2023/08/02 by Nastasi, Antonella, Camacho, Cintia Pacchiano · 3 citations
#30L99 #31E05 #35J60 #49N60 #Analysis of PDEs (math.AP) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2308.01221

Abstract

We prove boundedness, Hölder continuity, Harnack inequality results for local quasiminima to elliptic double phase problems of p-Laplace type in the general context of metric measure spaces. The proofs follow a variational approach and they are based on the De Giorgi method, a careful phase analysis and estimates in the intrinsic geometries.

Cited by

• On the Lavrentiev gap for manifold-valued maps
• Regularity for quasilinear elliptic equations in metric measure spaces
• Vectorial Double Phase Obstacle Problems

Related

• Boundary regularity for quasiminima of double-phase problems on metric spaces
• Gradient higher integrability for double phase problems on metric measure spaces
• New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems
• Removable sets in non-uniformly elliptic problems
• Hölder regularity for weak solutions to nonlocal double phase problems