Sub-Elliptic Boundary Value Problems for Quasilinear Elliptic Operators

Abstract

<p>Classical solvability and uniqueness in the Hölder space C^2+α(Ω¯) is proved for the oblique derivative problem</p>

<pre>{α^ij(x) D_iju + b(x, u, Du) = 0 in Ω,<br> ∂u / ∂ℓ = φ(x) on ∂Ω</pre>

<p>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.</p>