Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces

By B. Barrera, Alessio Figalli, Enrico Valdinoci. 2012

141 citations recorded by the source corpus.

We prove that C1,↵ s-minimal surfaces are of class C1. For this, we develop a new bootstrap regularity theory for solutions of integro-differential equations of very general type, which we believe is of independent interest.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9315dbe67ef5ce5d1f0113f55246420fcdf9eb4c

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Graph properties for nonlocal minimal surfaces (2015, background): “4 in [7], we have that ∂E is a graph of class C in the vicinity(1) of the origin – and, as a matter of fact, of class C∞, thanks to Theorem 1 of [2].”
Nonlocal Diffusion and Applications (2015, background): “See [82] for the proof of this results (as a matter of fact, in [82] only C regularity is proved, but then [5] proved that s-minimal sets with C-boundary are automatically C8).”
Regularity properties of nonlocal minimal surfaces via limiting arguments (2011, background): “For other recent regularity results for nonlocal minimal surfaces see [3,13].”
Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies (2014, background): “This allows us to address local and global minimality properties of balls with respect to the volume-constrained minimization of a free energy consisting of a nonlocal s-perimeter plus a non-local repulsive interaction term.”
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].”
Infinite Speed of Propagation and Regularity of Solutions to the Fractional Porous Medium Equation in General Domains (2015, background): “x; y; t/ that are C 2 in y, and [6] for the elliptic case.”