Regularity for minimizers for functionals of double phase with variable exponents

Partial Regularity for Minimizers of Quasi-convex Functionals with General Growth

holds for every A ∈ R and every smooth ξ : B1 → R with compact support in the open unit ball B1 in R . By Jensen’s inequality, quasi convexity is a generalization of convexity. It was originally introduced as a notion for proving the lower semicontinuity and the existence of minimizers of variational integrals. In fact, assuming a power growth condition, quasi convexity is proved to be a necess...

Γ-convergence of power-law functionals with variable exponents

Γ-convergence results for power-law functionals with variable exponents are obtained. The main motivation comes from the study of (first-failure) dielectric breakdown. Some connections with the generalization of the ∞-Laplace equation to the variable exponent setting are also explored. 2000 Mathematics Subject Classification:

Partial regularity for quasi minimizers

Sobolev and Lipschitz regularity for local minimizers of widely degenerate anisotropic functionals

We prove higher differentiability of bounded local minimizers to some widely degenerate functionals, verifying superquadratic anisotropic growth conditions. In the two dimensional case, we prove that local minimizers to a model functional are locally Lipschitz continuous functions, without any restriction on the anisotropy.

Energy Minimizers for Curvature-Based Surface Functionals

We compare curvature-based surface functionals by comparing the aesthetic properties of their minimizers. We introduce an enhancement to the original inline curvature variation functional. This new functional also considers the mixed cross terms of the normal curvature derivative and is a more complete formulation of a curvature variation functional. To give designers an intuitive feel for the ...