987 research outputs found
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 variations whose solutions can be viewed as such almost minimizers
Partial Regularity Results for Asymptotic Quasiconvex Functionals with General Growth
We prove partial regularity for minimizers of vectorial integrals of the
Calculus of Variations, with general growth condition, imposing quasiconvexity
assumptions only in an asymptotic sense
Higher Integrability for Constrained Minimizers of Integral Functionals with (p,q)-Growth in low dimension
We prove higher summability for the gradient of minimizers of strongly convex
integral functionals of the Calculus of Variations with (p,q)-Growth conditions
in low dimension. Our procedure is set in the framework of Fractional Sobolev
Spaces and renders the desired regularity as the result of an approximation
technique relying on estimates obtained through a careful use of difference
quotients.Comment: 22 pages, 0 figure
Optimal Lipschitz criteria and local estimates for non-uniformly elliptic problems
We report on new techniques and results in the regularity theory of general
non-uniformly elliptic variational integrals. By means of a new potential
theoretic approach we reproduce, in the non-uniformly elliptic setting, the
optimal criteria for Lipschitz continuity known in the uniformly elliptic one
and provide a unified approach between non-uniformly and uniformly elliptic
problems
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