A class of nonlinear elliptic boundary value problems

Details A class of nonlinear elliptic boundary value problems A class of nonlinear elliptic boundary value problems

2008-12-22

arxiv.org/abs/0812.4117v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper second order elliptic boundary value problems on bounded domains $\Omega\subset\dR^n$ with boundary conditions on $\partial\Omega$ depending nonlinearly on the spectral parameter are investigated in an operator theoretic framework. For a general class of locally meromorphic functions in the boundary condition a solution operator of the boundary value problem is constructed with the help of a linearization procedure. In the special case of rational Nevanlinna or Riesz-Herglotz functions on the boundary the solution operator is obtained in an explicit form in the product Hilbert space $L^2(\Omega)\oplus (L^2(\partial\Omega))^m$, which is a natural generalization of known results on $\lambda$-linear elliptic boundary value problems and $\lambda$-rational boundary value problems for ordinary second order differential equations.

Affiliated with

Also associated with

No associations

Rating

A class of nonlinear elliptic boundary value problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A class of nonlinear elliptic boundary value problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A class of nonlinear elliptic boundary value problems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-538530