Manifold Constrained Non-uniformly Elliptic Problems
By Cristiana De Filippis, Giuseppe Mingione. Journal of Geometric Analysis, 2019
90 citations recorded by the source corpus.
We consider the problem of minimizing variational integrals defined on 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. 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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/cf279d688a9194aeacb6206c1be6e8b51c2d1168
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Citations in the corpus
- Existence of solutions for singular double phase problems via the Nehari manifold method (2021, unknown): “We mention the papers of Baroni-Colombo-Mingione [4, 5, 6], Baroni-Kuusi-Mingione [7], Byun-Oh [9, 10], Byun-Youn [11], Colombo-Mingione [14, 15, 16], De Filippis-Mingione [18, 19, 20], De Filippis-Palatucci [21], EspositoLeonetti-Mingione [23], Esposito-Leonetti-Petricca [24], Marcellini [37, 38, 3”
- New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems (2022, background): “Moreover, recent results for nonuniformly elliptic variational problems and nonautonomous functionals can be found in the papers of Beck-Mingione [9, 10], De Filippis-Mingione [20, 21, 22, 23, 24] and Hästö-Ok [39].”