Free boundary regularity for a problem with right hand side

By D. Silva. 2009

137 citations recorded by the source corpus.

We consider a one-phase free boundary problem with variable coefficients and non-zero right hand side. We prove that flat free boundaries are $C^{1,\alpha}$ using a different approach than the classical supconvolution method of Caffarelli. We use this result to obtain that Lipschitz free boundaries are $C^{1,\alpha}$.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/20e41b718658d648afaa1c270e650f570a9b707d

How researchers see this paper

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In Applied Mathematics

1. Fausto Ferrari
2. Sandro Salsa
3. D. Silva
4. Luis Caffarelli
5. Juan Luis V'azquez
6. Xavier Ros-Oton
7. Pablo Raúl Stinga

In Computational Theory and Mathematics

1. Fausto Ferrari
2. Sandro Salsa
3. D. Silva
4. Juan Luis V'azquez
5. Pablo Raúl Stinga
6. Luis Caffarelli

In Numerical Analysis

1. Sandro Salsa
2. Fausto Ferrari

Citations in the corpus

• Two-phase problems with distributed sources: regularity of the free boundary (2012, methodology): “For another application of the techniques in [De Silva 2011] see also [Leitão and Teixeira 2011].”