partial-differential-equations-by-evans · Problem 11

Sobolev Spaces

Mathematics — Calculus · sobolev-spaces-difference-quotients

Problem

Show by example that if we have

\|D^h u\|_{L^1(V)} \leq C

for all

0 < |h| < \frac{1}{2}\mathrm{dist}(V, \partial U)

, it does not necessarily follow that

u \in W^{1,1}(V)