Schauder estimates for oblique derivative problems |
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| Affiliation: | 1. Centre of Geophysical, Data Studies and Mathematics Applications, of GIPE RAS, 3, ul. Molodezhnaya, 117296, Moscow, Russia;1. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics NASU, Lviv, 79060, Ukraine;2. Ivan Franko National University of Lviv, Lviv, 79000, Ukraine;3. Department of Civil Engineering, University of Siegen, Siegen, 57068, Germany;1. Laboratoire POems UMR 7231 CNRS-INRIA-ENSTA, ENSTA-UMA, 828 Bd des Maréchaux, 91762 Palaiseau Cedex, France;2. LAMFA UMR CNRS 7352, Université de Picardie Jules Verne, 33 rue Saint-Leu 80039 Amiens Cedex, France;3. LMAC EA 2222, Sorbonne universités, Université de technologie de Compiègne, CS 60 319 - 60 203 Compiègne cedex, France;1. Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133 Milano, Italy;2. School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK |
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| Abstract: | We prove that the solution of the oblique derivative parabolic problem in a noncylindrical domain ΩT belongs to the anisotropic Holder space C2+α, 1+α/2(gwT) 0 < α < 1, even if the nonsmooth “lateral boundary” of ΩT is only of class C1+α, (1+α)/2). As a corollary, we also obtain an a priori estimate in the Hölder space C2+α(Ω0) for a solution of the oblique derivative elliptic problem in a domain Ω0 whose boundary belongs only to the classe C1+α. |
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