Sub-Elliptic Boundary Value Problems for Quasilinear Elliptic Operators

Date

1997-01-08

Authors

Palagachev, Dian K.
Popivanov, Peter R.

Journal Title

Journal ISSN

Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

Abstract

Classical solvability and uniqueness in the Hölder space C2+α(Ω¯) is proved for the oblique derivative problem {αij(x) Diju + b(x, u, Du) = 0 in Ω, ∂u / ∂ℓ = φ(x) on ∂Ω in the case when the vector field ℓ(x) = (ℓ1(x),..., ℓn(x)) is tangential to the boundary ∂Ω at the points of some non-empty set S ⊂ ∂Ω, and the nonlinear term b(x, u, Du) grows quadratically with respect to the gradient Du.

Description

Keywords

Quasilinear elliptic operator, Degenerate oblique derivative problem, Sub-elliptic estimates

Citation

Palagachev, D. K., & Popivanov, P. R. (1997). Sub-elliptic boundary value problems for quasilinear elliptic operators. </i>Electronic Journal of Differential Equations, 1997</i>(01), pp. 1-12.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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