This was a question that arose for me when I was thinking about how one proves strong unique continuation for elliptic equations. I never could come up with a satisfactory answer. Background: When ...
I would like an example where the maximum principle fails in a bounded smooth domain $\Omega$ where one has a solution which is not $C^2(\Omega)$ to $Lu=0$ where $L$ is elliptic and linear. This ...
Weakened conditions on the smoothness of the domain in the regularity and a priori estimate of Agmon, Douglis, and Nirenberg for elliptic systems
I have read in a couple of places (e.g. An Introduction to PDEs by Renardy and Rogers, p.309) that the smoothness hypotheses on the domain in the a priori estimate of Agmon, Douglis, and Nirenberg for ...
I heard that De Giorgi-Nash-Moser type regularity arguments fail for elliptic systems, but do not know where to start looking for more substantial information. Why does the regularity fail? Is there ...