4
$\begingroup$

Could anyone suggest a textbook, article, or lecture notes that covers elliptic PDE theory (existence, uniqueness, regularity) on all of $\mathbb{R}^d$, as opposed to the Dirichlet or Neumann problem on some bounded subset? I emphasize I am interested in a treatment that concerns the elliptic operators with variable coefficients that precludes a Fourier transform based solution. I found that Krylov's textbook (Lectures on Elliptic and Parabolic Equations in Sobolev Spaces) treats the problem, but I was curious if there were any others.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
5
$\begingroup$

The following book might be helpful:

Elliptic Partial Differential Equations: Volume 1: Fredholm Theory of Elliptic Problems in Unbounded Domains by Vitaly Volpert (Birkhäuser, 2011)
http://books.google.com/books?isbn=3034605374

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .