A brief introduction to the method of boundary layer potentials

Marius Mitrea, University of Missouri-Columbia, USA

October 15-18, 2012

One of the most effective strategies for solving boundary value problems for large classes of partial differential equations is the method of boundary layer potentials. Its essence consists of reducing the entire original problem in a given domain \(D\) to solving an integral equation formulated entirely on the boundary of \(D\). This course is designed as a rapid introduction to this type of technology, with special emphasis on the role played by the tools of modern Harmonic Analysis, and in particular the theory of Singular Integral Operators of Calderón-Zygmund type, to this subject. More info

Topics in Geometric Analysis and Applications to PDEs

Dorina Mitrea, University of Missouri-Columbia, USA

October 22-25, 2012

Variation of area formulas for hypersurfaces in a Riemannian manifold are basic results in Riemannian geometry with fundamental implications in the theory of minimal surfaces. The goal of this course is to develop self-contained proofs of these results, corresponding to hypersurfaces in \(\mathbb{R}^n\), which have the attractive feature that they completely avoid the heavy differential geometrical jargon which typically accompanies much of the work on this topic. This requires that we pedantically develop a number of alternative tools. More info

Poster Poster
Organized by J.M Martell
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