Timeline for Extensions in parabolic Hölder spaces

9 events

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Nov 20, 2014 at 14:25	comment	added	Andrew		For $k\ge2$ it's theorem 5.2 from ch. 4 of [O. A. Ladyzenskaja, V. A. Solonnikov, and N. N. Uralceva, Linear and Quasi–Linear Equations of Parabolic Type]. For $k=1$ [E. A. Baderko, Mathematical Methods in the Applied Sciences, V. 20, #5], $k=0$ [A.N. Konenkov, Differential Equations, 2004, V. 40, #3].
Nov 20, 2014 at 13:56	comment	added	foo90		Thank you. And last thing, do you have a reference the existence result for the first BVP you invoke?
Nov 20, 2014 at 13:32	history	edited	Andrew	CC BY-SA 3.0	added 291 characters in body
Nov 20, 2014 at 13:27	comment	added	Andrew		@foo90 Yes, you are right. So here is another way to satisfy compatibility conditions. I've rewritten the answer, it was too long for a comment.
Nov 17, 2014 at 13:05	comment	added	Andrew		The existence result for the first BVP is used. If $\varphi\in C^{\frac{k+\alpha}{2};k+\alpha}([0,T]\times\partial\Omega)$, the compatibility conditions hold etc, then there exists a solution from $C^{\frac{k+\alpha}{2};k+\alpha}(\bar Q)$.
Nov 17, 2014 at 12:44	comment	added	foo90		Thank you. When you say that the solution $u$ of the BVP belongs to $C^{\frac{k+\alpha}{2};k+\alpha}(\bar Q)$, you use the parabolic Schauder esitimates?
Nov 17, 2014 at 12:38	vote	accept	foo90
Nov 17, 2014 at 8:17	history	edited	Andrew	CC BY-SA 3.0	deleted 23 characters in body
Nov 17, 2014 at 8:11	history	answered	Andrew	CC BY-SA 3.0