A hyperbolic mixed initial boundary-value problem is investigated in which the Neumann condition and the Dirichlet condition are given on complementary parts of the boundary. An existence and uniqueness result in Sobolev spaces with additional differentiation in the tangential directions to the inte
The Dirichlet problem for second order parabolic operators in non-cylindrical domains
✍ Scribed by Roberto Argiolas; Anna Piro Grimaldi
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 254 KB
- Volume
- 283
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
In this paper we develope a perturbation theory for second order parabolic operators in non‐divergence form. In particular we study the solvability of the Dirichlet problem in non cylindrical domains with L^p^ ‐data on the parabolic boundary (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
📜 SIMILAR VOLUMES
We study the Dirichlet problem for the parabolic equation u t = u m m > 0, in a bounded, non-cylindrical and non-smooth domain ⊂ N+1 N ≥ 2. Existence and boundary regularity results are established. We introduce a notion of parabolic modulus of left-lower (or left-upper) semicontinuity at the points
## Abstract We consider the Dirichlet problem for non‐divergence parabolic equation with discontinuous in __t__ coefficients in a half space. The main result is weighted coercive estimates of solutions in anisotropic Sobolev spaces. We give an application of this result to linear and quasi‐linear p
## S 1. Introduction and statement of the results 1. The full proofs of the results stated in [18] are given in this paper. We consider the mixed problem (or the init,ial boundary value problem) for a second order strictly hyperbolic operator with a singular oblique derivative. This is the case wh