The method of layer potentials in L^p and endpoint spaces for elliptic operators with L^∞ coefficients

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• Andrew Morris (University of Oxford)
• Wednesday 06 November 2013, 16:00-17:00
• Room R17/18, Watson building.

If you have a question about this talk, please contact José Cañizo.

We consider the layer potentials associated with operators L=- div A ∇ acting in the upper half-space Rⁿ⁺¹₊, n≥ 2, where the coefficient matrix A is complex, elliptic, bounded, measurable, and t-independent. A “Calderón-Zygmund” theory is developed for the boundedness of the layer potentials under the assumption that solutions of the equation Lu=0 satisfy interior De Giorgi-Nash-Moser type estimates. In particular, we prove that L² estimates for the layer potentials imply sharp L^p and endpoint space estimates. The method of layer potentials is then used to obtain solvability of boundary value problems. This is joint work with Steve Hofmann and Marius Mitrea.

This talk is part of the Analysis Seminar series.

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• Analysis Seminar
• Room R17/18, Watson building
• School of Mathematics Events

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