Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am gathering material that contains results of regularity for solutions of the equation \begin{equation} \mbox{div}(A(x) \nabla u) = f \end{equation} where the coefficints $a_{i,j}$ of $A$ are only measurable and $f \in L^p$ for some $p \in \mathbb{N}$ and \begin{equation} \lambda |\xi|^{2} \le \langle A(x)\xi , \xi \rangle \le |\xi|^{2} \quad \forall x,\xi \end{equation}. Can you give me some references? Assume others hypothesis if you want. Thank you.

share|cite|improve this question
The paper "Besov regularity of elliptic boundary value problems" by Dahlke and Devore is quite insightful in the case where A=const but f and the shape of the domain boundary are rough. – Nick Alger Jul 2 '12 at 23:00
up vote 1 down vote accepted
  1. Ladyzhenskaya & Uraltseva, "Linear and quasilinear elliptic equations"
  2. Gilbarg & Trudinger, "Elliptic PDE of second order"
  3. Maly & Ziemer, "Fine regularity of solutions of elliptic PDE"
  4. Heinonen, Kilpelainen, Martio "Nonlinear potential theory of degenerate elliptic equations"

Listed in approximate order of relevance to the question. The books 3 & 4 deal more with p-Laplace type equations, but you can still get something by setting $p=2$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.