987 research outputs found

    Partial regularity for almost minimizers of quasi-convex integrals

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    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

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    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

    Partial Regularity for Holonomic Minimisers of Quasiconvex Functionals

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    Higher Integrability for Constrained Minimizers of Integral Functionals with (p,q)-Growth in low dimension

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    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

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    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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