In this paper we prove, by showing that solutions have exactly the same degree of regularity as the obstacle, optimal regularity results for obstacle problems involving evolutionary p-Laplace type operators. A main ingredient, of independent interest, is a new intrinsic interpolative geometry allowing for optimal linearization principles via blow-up analysis at contact points. This also opens the way to the proof of a removability theorem for solutions to evolutionary p-Laplace type equations. A basic feature of the paper is that no differentiability in time is assumed on the obstacle; this is in line with the corresponding linear results.

Sharp regularity for evolutionary obstacle problems, interpolative geometries and removable sets / T., Kuusi; Mingione, Giuseppe; K., Nystrom. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 101:2(2014), pp. 119-151. [10.1016/j.matpur.2013.03.004]

Sharp regularity for evolutionary obstacle problems, interpolative geometries and removable sets

MINGIONE, Giuseppe
;
2014-01-01

Abstract

In this paper we prove, by showing that solutions have exactly the same degree of regularity as the obstacle, optimal regularity results for obstacle problems involving evolutionary p-Laplace type operators. A main ingredient, of independent interest, is a new intrinsic interpolative geometry allowing for optimal linearization principles via blow-up analysis at contact points. This also opens the way to the proof of a removability theorem for solutions to evolutionary p-Laplace type equations. A basic feature of the paper is that no differentiability in time is assumed on the obstacle; this is in line with the corresponding linear results.
2014
Sharp regularity for evolutionary obstacle problems, interpolative geometries and removable sets / T., Kuusi; Mingione, Giuseppe; K., Nystrom. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 101:2(2014), pp. 119-151. [10.1016/j.matpur.2013.03.004]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2741102
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