Lewis, J., Lindqvist, P., Manfredi, J.J., Salsa, S.
Lewis, John, Gianazza, Ugo Pietro (Eds.)
2012, XI, 247 p. 3 illus.
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The notes trace a timely overview of the main issues in the regularity theory for degenerate and singular elliptic and parabolic PDEs
The deep connections among seemingly unrelated topics are shown
The main results are thoroughly discussed and proper counterexamples are presented
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.
Content Level »Research
Keywords »35J70, 35J75, 35J92, 35K65, 35K67, 35K86, 35K92, 49K20, 49N60 - Boundary Harnack Inequalities - Fractional Laplacian - Obstacle Problem - Random Tug-of-war Games - Supersolutions to degenerate parabolic equatons