The tag has no wiki summary.

learn more… | top users | synonyms

2
votes
1answer
401 views

Sobolev imbedding

It is known that, for $n \ge 3, 2 < p< 2^*$, the imbedding $H^1(\mathbb{R}^n) \hookrightarrow L^p(\mathbb{R}^n)$ is not compact. Let $G=O(n_1) \times O(n_2)\times\cdots\times O(n_k)$, with ...
8
votes
4answers
1k views

Trace theorem for $C^{k,1}$ domains

What are the best results on (Sobolev space) trace theorems for $C^{k,1}$ domains? For $k=0$, e.g., when the domain is Lipschitz, from e.g. the works of Martin Costabel and Zhonghai Ding, it is known ...
2
votes
1answer
774 views

Sobolev-Slobodeckij spaces for p=infinity

For $1\leq p<\infty$ an approach to define fractional Sobolev spaces is by Sobolev-Slobodeckij spaces a generalisation of Hölder continuity. For example letting $U\subset\mathbb{R}^n$ then, $ ...
0
votes
0answers
266 views

Gradient of the energy functional in $H^{1,2}$-norm

I have to use estimates for the gradient of the energy functional on the free loop space of a fixed compact manifold $Q$. As such, one considers $H^{1,2}$-maps of the circle into $Q$. The energy ...