Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options not deleted user 37103

regularity of solutions of PDEs.

11 votes
2 answers
3k views

What's wrong with the Courant nodal domain theorem?

However, Chavel in Eigenvalues in Riemannian Geometry seems to point out (P23) that Divergence theorem is used, so the regularity of the nodal set matters, whose proof by Cheng in dimension $\ge 3$ is …
Fan Zheng's user avatar
  • 5,169
2 votes

Moser estimates?

. $$ (If $u$ does not have $W^{1,2}$ regularity to start with, you can approximate the left hand side by difference quotients.) Now do the same for $\nabla u$, $\nabla^2 u$, etc. …
Fan Zheng's user avatar
  • 5,169
2 votes

Elliptic theory on compact manifolds

For the specific question of getting rid of the low-order term $\|u\|_p$, what you really need is the compact embedding of $W^{2,p}$ in $L^p$ (Rellich–Kondrachov theorem). Indeed, suppose there is no …
Fan Zheng's user avatar
  • 5,169