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2005 On $L_p$ estimates of optimal type for the parabolic oblique derivative problem with {VMO} coefficients
Peter Weidemaier
Differential Integral Equations 18(8): 935-946 (2005).

Abstract

We generalize recent results by L.G. Softova concerning $ W_p^{2,1} (\Omega_T) $ estimates ($ 1 < p < \infty$) for second order parabolic operators with VMO coefficients and the boundary condition $$ \sum_{i=1}^n b_i(\xi,t) \partial_i u(\xi,t) = g(\xi,t) \ \ \text{ on $ \partial \Omega_T $} $$ in the nondegenerate case (see Remark 2.2 i). While Softova assumed $ [(\xi,t) \mapsto b_i(\xi,t)] \in Lip(\partial \Omega_T) $, we weaken this assumption to $ b_i \in C^{ \alpha, \alpha/2 } (\partial \Omega_T) $ for some $ \alpha > 1 -1/p $.

Citation

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Peter Weidemaier. "On $L_p$ estimates of optimal type for the parabolic oblique derivative problem with {VMO} coefficients." Differential Integral Equations 18 (8) 935 - 946, 2005.

Information

Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35194
MathSciNet: MR2150446

Subjects:
Primary: 35K20
Secondary: 35B45 , 35R05

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.18 • No. 8 • 2005
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