All Questions
7 questions with no upvoted or accepted answers
5
votes
0
answers
445
views
Why are functions with vanishing normal derivative dense in smooth functions?
Question
Let $M$ be a compact Riemannian manifold with piecewise smooth boundary. Why are smooth functions with vanishing normal derivative dense in $C^\infty(M)$ in the $H^1$ norm?
Here I define $...
- 881
4
votes
0
answers
143
views
Sobolev space of maps between manifolds with boundary
Let $(M,g)$ and $(N,h)$ be compact Riemannian manifolds with non-empty smooth boundary.
If we consider the Sobolev space $W^{1,p}(M,N)$, is there a reference
on how to model this as a manifold?
If ...
- 3,423
3
votes
0
answers
411
views
Bounded functions dense in Sobolev Spaces
Let $M$ be a complete Riemannian manifold. Is it always true that the subspace $C^2_b(M)\cap W^{2,p}(M)$ is dense in $W^{2, p}(M)$, where $C^2_b(M)$ denotes the space of functions that are uniformly ...
- 9,853
2
votes
0
answers
92
views
Sharp Sobolev trace inequalities on Riemannian manifolds with boundaries
For $n \geq3$, let $(M,g)$ be smooth $n$-dimensional, compact, Riemannian manifold with a smooth boundary. Then there exists some constant $A=A(M,g)>0$ such that, for all $u \in H^1(M)$
\begin{...
- 101
2
votes
0
answers
188
views
Self-adjointness of fractional laplacian
Lets consider the following functional analytic definition of the fractional Laplacian: Consider a (complete, connected, oriented) Riemannian manifold $(M,g)$ with corresponding Laplacian $\Delta_{g}$....
- 1,171
1
vote
0
answers
128
views
Self-ajointness of the Laplacian over a Riemannian manifold with boundary
I have some doubts about on a passage found on this article (https://arxiv.org/pdf/1510.08136.pdf).
Let
$(M,g)$ be a Riemannian manifold with boundary;
$E\to M$ be an hermitian fiber bundle;
$\Delta$ ...
- 141
1
vote
0
answers
198
views
Sobolev embedding in complete manifold
Let $(M,g)$ be a complete Riemannian $m$-manifold, with bounded geometry and $m\geq2$. Suppose that $(M,g)$ admits a bounded geometry.
Q Can we show that for $k-\frac{m}{p}\geq l-\frac{m}{q}$, we ...
- 1,915