Manifold constrained non-uniformly elliptic problems

Cristiana De Filippis; Giuseppe Mingione

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arXiv · 1903.08854

Manifold constrained non-uniformly elliptic problems

Cristiana De Filippis·Giuseppe Mingione

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Abstract

We consider the problem of minimizing variational integrals defined on \cc{nonlinear} Sobolev spaces of competitors taking values into the sphere. The main novelty is that the underlying energy features a non-uniformly elliptic integrand exhibiting different polynomial growth conditions and no homogeneity. We develop a few intrinsic methods aimed at proving partial regularity of minima and providing techniques for treating larger classes of similar constrained non-uniformly elliptic variational problems. In order to give estimates for the singular sets we use a general family of Hausdorff type measures following the local geometry of the integrand. A suitable comparison is provided with respect to the naturally associated capacities.

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Cristiana De Filippis, Giuseppe Mingione. 2019-03-21. Manifold constrained non-uniformly elliptic problems. https://arxiv.org/abs/1903.08854

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