Regularity Estimates for Nonlinear Elliptic and Parabolic Problems: Cetraro, Italy 2009 <p>Editors: Ugo Gianazza, John Lewis</p>The issue of regularity has played a central role in the theory of Partial Differential Equations almost since its inception, and despite the tremendous advances made it still remains a very fruitful research field. In particular considerable strides have been made in regularity estimates for degenerate and singular elliptic and parabolic equations over the last several years, and in many unexpected and challenging directions. Because of all these recent results, it seemed high time to create an overview that would highlight emerging trends and issues in this fascinating research topic in a proper and effective way. The course aimed to show the deep connections between these topics and to open new research directions through the contributions of leading experts in all of these fields. |
Contents
Applications of Boundary Harnack Inequalities for p Harmonic Functions and Related Topics | 1 |
Regularity of Supersolutions | 73 |
Introduction to Random TugofWar Games and PDEs | 132 |
The Problems of the Obstacle in Lower Dimension and for the Fractional Laplacian | 153 |
List of Participants | 245 |
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assume B(en B₁ ball blow-up boundary Harnack inequality bounded comparison principle constant converges convex deduce defined divergence form dx dt elliptic equations elliptic operators exists follows global solution H-dim harmonic functions harmonic measure Harnack inequality Hölder continuous homogeneous implies infimal convolutions integral Laplace Laplace operator Laplacian Lemma Lipschitz continuity Lipschitz domain lower semicontinuous martingale Math maximum principle Moreover nonlinear NTA domain obtain optimal regularity p-harmonic p-superharmonic function polynomial positive p harmonic proof of Theorem prove Theorem Reifenberg flat satisfies sequence Signorini problem Sobolev Sobolev space subsolution Suppose tangential test function Theorem 3.1 thin obstacle problem uniformly v(xo vanishing viscosity supersolution weak solution weak supersolution zero thin obstacle