Analysis Seminar
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Analysis Seminar – Simon Bortz (University of Alabama)
Analysis Seminar – Simon Bortz (University of Alabama)
Title: A free boundary problem for the heat equation. Abstract: In his breakthrough result, it was shown by Dahlberg that the L^2 Dirichlet problem for the Laplacian (harmonic functions) is solvable in the region above a Lipschitz graph. Dahlberg did this by showing a local reverse Hölder inequality for the Poisson kernel in such domains.
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Analysis Seminar – Armin Schikorra (University of Pittsburgh)
Analysis Seminar – Armin Schikorra (University of Pittsburgh)
Title: A Harmonic Analysis perspective on $W^{s,p}$ as $s \to 1^-$. Abstract: We revisit the Bourgain-Brezis-Mironescu result that the Gagliardo-Norm of the fractional Sobolev space W^{s,p}, up to rescaling, converges to W^{1,p} as s\to 1. We do so from the perspective of Triebel-Lizorkin spaces, by finding sharp $s$-dependencies for several embeddings between $W^{s,p}$ and $F^{s,p}_q$