Degenerate elliptic boundary value problems with asymptotically linear nonlinearity

Quasi-linear elliptic boundary value problems

Elliptic Boundary-Value Problems

In the first part of this chapter we focus on the question of well-posedness of boundary-value problems for linear partial differential equations of elliptic type. The second part is devoted to the construction and the error analysis of finite difference schemes for these problems. It will be assumed throughout that the coefficients in the equation, the boundary data and the resulting solution ...

Linear and nonlinear degenerate boundary value problems in Besov spaces

Keywords: Boundary value problems Differential-operator equations Banach-valued Besov spaces Operator-valued multipliers Interpolation of Banach spaces a b s t r a c t The boundary value problems for linear and nonlinear degenerate differential-operator equations in Banach-valued Besov spaces are studied. Several conditions for the separability of linear elliptic problems are given. Moreover, t...

Sub - Elliptic Boundary Value Problems Forquasilinear Elliptic

Classical solvability and uniqueness in the HH older space C 2+ () is proved for the oblique derivative problem a ij (x)D ij u + b(x; u; Du) = 0 in ; @u=@`= '(x) on @ in the case when the vector eld`(x) = (` 1 (x); : : : ; ` n (x)) is tangential to the boundary @ at the points of some non-empty set S @; and the nonlinear term b(x; u; Du) grows quadratically with respect to the gradient Du. 0. I...

Nonlinear Elliptic Boundary Value Problems

It is the object of the present note to present a new nonlinear version of the orthogonal projection method for proving the existence of solutions of nonlinear elliptic boundary value problems. The key point in this method is the application of a new general theorem concerning the solvability of nonlinear functional equations in a reflexive Banach space involving operators which may not be cont...