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