A density result for Sobolev spaces in dimension two, and applications to stability of nonlinear Neumann problems

Details A density result for Sobolev spaces in dimension two, and applications to stability of nonlinear Neumann problems A density result for Sobolev spaces in dimension two, and applications to stability of nonlinear Neumann problems

2005-10-27

arxiv.org/abs/math/0510590v1

Mathematics

Analysis of PDEs

24 pages

Scientific paper

We prove that if $\Om \subseteq \R^2$ is bounded and $\R^2 \setminus \Om$ satisfies suitable structural assumptions (for example it has a countable number of connected components), then $W^{1,2}(\Om)$ is dense in $W^{1,p}(\Om)$ for every $1\le p<2$. The main application of this density result is the study of stability under boundary variations for nonlinear Neumann problems of the form $$ \begin{cases} -{\rm div} A(x,\nabla u)+B(x,u)=0 & \text{in}\Om, \\ A(x,\nabla u)\cdot \nu=0 & \text{on}\partial \Om, \end{cases} $$ where $A:\R^2\times \R^2 \to \R^2$ and $B:\R^2 \times \R \to \R$ are Carath\'eodory functions which satisfy standard monotonicity and growth conditions of order $p$.

Affiliated with

Also associated with

No associations

Rating

A density result for Sobolev spaces in dimension two, and applications to stability of nonlinear Neumann 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 density result for Sobolev spaces in dimension two, and applications to stability of nonlinear Neumann problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A density result for Sobolev spaces in dimension two, and applications to stability of nonlinear Neumann problems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-322848