Nonlocal self-improving properties

By Tuomo Kuusi, Giuseppe Mingione, Yannick Sire. 2015

152 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/dfdb9a8e49a8fa6367388d6da9de4e1120bc8515

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In Applied Mathematics

Citations in the corpus

The obstacle problem for nonlinear integro-differential operators (2016, background): “Nevertheless, some related regularity results have been very recently achieved in this context, in [4,12,23,13,25,26,27,28,41] and many others, where often a fundamental role to understand the nonlocality of the nonlinear operators L has been played by a special quantity,”
On a fractional degenerate Kirchhoff-type problem (2017, background): “The papers [23, 24] contain some recent nice results on nonlocal fractional problems as well.”
Stability of variational eigenvalues for the fractional p−Laplacian (2015, background): “Many efforts have been devoted to the study of problems involving the fractional p−Laplacian operator, among which we mention eigenvalue problems [7, 21, 27, 30], regularity theory [14, 26, 28, 29] and existence of solutions within the framework of Morse theory [25].”
Interior regularity of solutions of non-local equations in Sobolev and Nikol’skii spaces (2016, result): “Also, the very recent [KMS15] provides higher differentiability/integrability in a nonlinear setting quite similar to ours.”
Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: A unified approach via fractional De Giorgi classes (2016, background): “3) have already been obtained by many authors (see for instance [27, 43, 9]).”
Nonlinear commutators for the fractional p-Laplacian and applications (2015, unknown): “[18] T. Kuusi, G. Mingione, and Y. Sire.”
Fractional Orlicz-Sobolev embeddings (2020, background): “A touch of recent contributions in this connection is furnished by [7, 8, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 41, 44, 45, 51, 52, 53, 58, 59, 61, 62, 63, 64, 65, 68, 70, 71, 77, 76, 78, 83, 86].”
Hölder regularity for weak solutions to nonlocal double phase problems (2021, background): “We refer to, for instance, [7, 25, 26, 31, 39, 40, 41, 42, 44] for regularity results for nonlocal linear equations with fractional orders.”
Ground state solutions of scalar field fractional Schrödinger equations (2015, background): “We alsomention here, for completeness, some very interesting regularity results for fractional problems proved recently in [29,30].”
Fractional double-phase patterns: concentration and multiplicity of solutions (2020, background): “The corresponding nonlocal version can be found emulating the nonlinear operators considered in [50].”
Hölder regularity for nonlocal double phase equations (2019, unknown): “For this, one should extend the recent nonlocal Gehring-type theorems proven in [24,34].”