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seen Sep 13 at 7:28

Sep
7
comment Boundary regularity of Dirichlet Eigenfunction on bounded domains
Thank you very much! @Christian: Why should there be a problem? Do you have an exceptional situation in mind?
Sep
6
asked Boundary regularity of Dirichlet Eigenfunction on bounded domains
Aug
7
comment construction of heat kernels for non-compact manifolds with boundary
Did you find an answer to your question in meanwhile? I'm wondering, if one can construct the dirichlet heat kernel for unbounded domains with boundary this way (e.g. unbounded domains in euclidean space).
Aug
4
comment Existence of the Dirichlet heat kernel for arbitrary open subsets?
@Chrisitan: Thank you! What do you mean by $e^{t\Delta}$? In my experience this symbol occurs in two situations. First in the context of 'continuous functional calculus'. And second in the theory of 'strongly continuous semigroups'. Maybe all of them correspond to the same operator, but I'm not sure. I would be very glad, if you can explain it to me?
Aug
3
accepted How to evaluate the wiener measure of sets?
Aug
3
asked Existence of the Dirichlet heat kernel for arbitrary open subsets?
Jul
14
comment How to evaluate the wiener measure of sets?
Thank you very much for your help! I have to think some time about your approach and probably will tell you whether it helps.
Jul
14
comment How to evaluate the wiener measure of sets?
@Nate Eldredge: I want to know the measure of the set G (which I wrote down above), which is quite explicit. Don"t you think so?
Jul
14
comment How to evaluate the wiener measure of sets?
@Kjos-Hanssen: Why do you mean the set can't be a Borel set?
Jul
14
comment How to evaluate the wiener measure of sets?
@Martin Hairer: Thank you very much for your comment. I will consider the construction via Kolmogorov soon. But I'm not a probabilist.
Jul
13
asked How to evaluate the wiener measure of sets?
May
8
accepted The first eigenvalue of the Schrödinger operator is simple.
May
8
accepted What is the right initial domain for the Dirichlet-Laplacian on a bounded domain?
Jan
4
comment What is the right initial domain for the Dirichlet-Laplacian on a bounded domain?
Ok thank you. So I assume that the Friedrichs extension of $-\Delta:C^{\infty}_0 (\Omega)\subset L^2(\Omega)\rightarrow L^2(\Omega)$ is equal to the other one. Is that right?
Jan
4
asked What is the right initial domain for the Dirichlet-Laplacian on a bounded domain?
Jul
27
awarded  Disciplined
Jul
25
awarded  Yearling
Jul
24
awarded  Commentator
Jun
26
accepted Eigenfunctions of Schrödinger Operators on the boundary
Jun
22
comment Eigenfunctions of Schrödinger Operators on the boundary
What do you mean by "test functions". Smooth functions with compact support (in our case this would mean all smooth functions)?