Palagachev, Dian K.Popivanov, Peter R.2018-08-282018-08-281997-01-08Palagachev, 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. 1-12.1072-6691https://hdl.handle.net/10877/7633Classical 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.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalQuasilinear elliptic operatorDegenerate oblique derivative problemSub-elliptic estimatesArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.