$W^{2,p}$-A~priori estimates for the neutral Poincar\'e problem

Dian K. Palagachev

$W^{2,p}$-A~priori estimates for the neutral Poincar\'e problem

Analysis of PDEs 2011-10-12 v1

Authors: Dian K. Palagachev

Abstract

A degenerate oblique derivative problem is studied for uniformly elliptic operators with low regular coefficients in the framework of Sobolev's classes $W^{2,p}(\Omega)$ for {\em arbitrary} $p>1.$ The boundary operator is prescribed in terms of a directional derivative with respect to the vector field $\l$ that becomes tangential to $\partial \Omega$ at the points of some non-empty subset $\E\subset \partial \Omega$ and is directed outwards $\Omega$ on $\partial\Omega\setminus\E.$ Under quite general assumptions of the behaviour of $\l,$ we derive {\it a priori} estimates for the $W^{2,p}(\Omega)$ -strong solutions for any $p\in(1,\infty).$

Keywords

operator theory and elliptic operators elliptic partial differential equations gradient estimates

Cite

@article{arxiv.1110.2469,
  title  = {$W^{2,p}$-A~priori estimates for the neutral Poincar\'e problem},
  author = {Dian K. Palagachev},
  journal= {arXiv preprint arXiv:1110.2469},
  year   = {2011}
}

Comments

This is the definitive version of a lecture delivered at the International Conference on "Recent Advances in PDEs" in memory of Filippo Chiarenza, Messina, December 15--17, 2005; 6 figures

$W^{2,p}$-A~priori estimates for the neutral Poincar\'e problem

Abstract

Keywords

Cite

Comments

Related papers