W
2,p
-a priori estimates for the emergent Poincaré Problem |
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Authors: | Dian K Palagachev |
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Institution: | (1) Dipartimento di Matematica, Politecnico di Bari, Via E. Orabona, 4, 70 125 Bari, Italy |
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Abstract: | We derive W
2,p
(Ω)-a priori estimates with arbitrary
p ∈(1, ∞), for the solutions of a degenerate oblique derivative problem for linear uniformly elliptic operators with low regular
coefficients. The boundary operator is given in terms of directional derivative with respect to a vector field ℓ that is tangent
to ∂Ω at the points of a non-empty set ε ⊂ ∂Ω and is of emergent type on ∂Ω.
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Keywords: | Uniformly elliptic operator Poincaré problem Emergent vector field Strong solution A priori estimates L p -Sobolev spaces |
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