Calendar of Events
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Colloquium – Chi-Wang Shu (Brown University)
Colloquium – Chi-Wang Shu (Brown University)
Title: High order numerical methods for hyperbolic equations Abstract: Hyperbolic equations are used extensively in applications including fluid dynamics, astrophysics, electro-magnetism, semi-conductor devices, and biological sciences. High order accurate numerical methods are efficient for solving such partial differential equations, however they are difficult to design because solutions may contain discontinuities. In this talk we will
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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 $F^{s,p}_q$