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Geometric Tangential Analysis and Sharp Regularity for Degenerate pdes

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Harnack Inequalities and Nonlinear Operators

Part of the book series: Springer INdAM Series ((SINDAMS,volume 46))

Abstract

We provide a broad overview on qualitative versus quantitative regularity estimates in the theory of degenerate parabolic pdes. The former relates to DiBenedetto’s revolutionary method of intrinsic scaling, while the latter is achieved by means of what has been termed geometric tangential analysis. We discuss, in particular, sharp estimates for the parabolic p −Poisson equation, for the porous medium equation and for the doubly nonlinear equation.

To Emmanuele DiBenedetto, with admiration and friendship, on the occasion of his 70th birthday.

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Acknowledgements

J.M.U. partially supported by the Center for Mathematics of the University of Coimbra, UID/MAT/00324/2013, funded by the Portuguese government through FCT/MCTES and co-funded by the European Regional Development Fund through Partnership Agreement PT2020.

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Correspondence to José Miguel Urbano .

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Teixeira, E.V., Urbano, J.M. (2021). Geometric Tangential Analysis and Sharp Regularity for Degenerate pdes. In: Vespri, V., Gianazza, U., Monticelli, D.D., Punzo, F., Andreucci, D. (eds) Harnack Inequalities and Nonlinear Operators. Springer INdAM Series, vol 46. Springer, Cham. https://doi.org/10.1007/978-3-030-73778-8_9

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