Regularity for almost-minimizers of variable coefficient Bernoulli-type functionals

Partial Regularity for Almost Minimizers of Quasi-Convex Integrals

We consider almost minimizers of variational integrals whose integrands are quasiconvex. Under suitable growth conditions on the integrand and on the function determining the almost minimality, we establish almost everywhere regularity for almost minimizers and obtain results on the regularity of the gradient away from the singular set. We give examples of problems from the calculus of variatio...

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.

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...

Almost multiplicative linear functionals and approximate spectrum

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...