Regularity in a one-phase free boundary problem for the fractional Laplacian
By D. Silva, Jean-Michel Roquejoffre. 2011
50 citations recorded by the source corpus.
For a one-phase free boundary problem involving a fractional Laplacian, we prove that "flat free boundaries" are $C^{1,\alpha}$. We recover the regularity results of Caffarelli for viscosity solutions of the classical Bernoulli-type free boundary problem with the standard Laplacian.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/0a20040f39c639e9ef268f35263018dbf0eca53f
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In Applied Mathematics
- Fausto Ferrari
- Sandro Salsa
- D. Silva
- Ovidiu Savin
- Luis Caffarelli
- Luis Silvestre
- Enrico Valdinoci
- Alessio Figalli
Citations in the corpus
- Two-phase problems with distributed sources: regularity of the free boundary (2012, methodology): “This method has been successfully applied in [De Silva and Roquejoffre 2012] to nonlocal one phase Bernoulli type problems, governed by the fractional Laplacian.”
- Boundary Harnack estimates in slit domains and applications to thin free boundary problems (2014, methodology): “nal set P ⊂ {xn+1 = 0} (slit), with Ck,α boundary in Rn, Γ := ∂RnP, k ≥ 1. In [DS3] we investigated the higher regularity of the free boundary for the thin one-phase free boundary problem (see [CRS], [DR], [DS1], [DS2]). In particular we developed a Schauder type estimate in slit domains, see Theore”