Regularity for general functionals with double phase

2017/08/30 by Baroni, Paolo, Colombo, Maria, Mingione, Giuseppe · 18 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.09147

Abstract

We prove sharp regularity results for a general class of functionals of the type w ↦ ∫ F(x, w, Dw) dx , featuring non-standard growth conditions and non-uniform ellipticity properties. The model case is given by the double phase integral w ↦ ∫ b(x,w)(|Dw|^p+a(x)|Dw|^q) dx , 1

Cited by

• Regularity for mixed-order nonlinear fractional equations with degenerate coefficients
• Double phase flow under Lavrentiev phenomenon
• Global boundedness of weak solutions with finite energy to a general class of Dirichlet problems
• On the Lavrentiev gap for manifold-valued maps
• Gradient higher integrability of bounded solutions to parabolic double-phase systems
• Interior C^1,α regularity of mixed local-nonlocal (p,q)-energy minimizers for p≤ sq
• Regularity for minimizers of degenerate, non-autonomous, orthotropic integral functionals
• Self-improving property for certain degenerate functionals with generalized Orlicz growth
• Higher integrability for parabolic PDEs with generalized Orlicz growth
• Bounded solutions and interpolative gap bounds for degenerate parabolic double phase problems
• Local boundedness of weak solutions to elliptic equations under unbalanced Orlicz growth conditions
• μ-ellipticity and nonautonomous integrals
• Partial regularity for parabolic systems of double phase type
• A Class of De Giorgi Type and Hölder Continuity for Some Problems in Musielak-Orlicz-Sobolev Spaces
• Sketches of Nonuniformly Elliptic Schauder Theory
• Smoothness of weight sharply discards Lavrentiev's gap for double phase functionals
• Vectorial Double Phase Obstacle Problems
• Gradient regularity for double-phase orthotropic functionals

Related

• Regularity results for mixed local and nonlocal double phase functionals
• Partial regularity for degenerate systems of double phase type
• Regularity for Orlicz phase problems
• Hölder regularity for weak solutions to nonlocal double phase problems
• Smoothness of weight sharply discards Lavrentiev's gap for double phase functionals