We present some new a priori estimates of the solutions to the second-order elliptic and parabolic interface problems. The novelty of these estimates lies in the explicit appearance of the discontinuous coefficients and the jumps of coefficients across the interface.
A priori estimates for fluid interface problems
β Scribed by Jalal Shatah; Chongchun Zeng
- Publisher
- John Wiley and Sons
- Year
- 2008
- Tongue
- English
- Weight
- 254 KB
- Volume
- 61
- Category
- Article
- ISSN
- 0010-3640
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π SIMILAR VOLUMES
## Abstract This note bridges the gap between the existence and regularity classes for the thirdβgrade RivlinβEricksen fluid equations. We obtain a new global __a priori__ estimate, which conveys the precise regularity conditions that lead to the existence of a global in time regular solution. Copy
Global L Ο± bound and uniqueness results about the Dirichlet problem, yβ¬u q β£ u s u Ε½ nq2.rΕ½ ny2. , u G 0 in β, u s 0 on Ρ¨ β, are obtained, where β ; β«ήβ¬ n Ε½ . Ε½ . n G 3 is a bounded smooth domain and β£ g 0, is close to , the first 1 1 eigenvalue of yβ¬ with Dirichlet boundary condition.