Name
Title | ||
|---|---|---|
Heat trace asymptotics and boundedness in the second order Sobolev space of isospectral potentials for the Dirichlet Laplacian. |
Abstract | ||
|---|---|---|
Let Omega be a C-infinity-smooth bounded domain of R-n, n >= 1, and let the matrix a is an element of C-infinity ((Omega) over bar; R-n2) be symmetric and uniformly elliptic. We consider the L-2(Omega)-realization A of the operator -div(a del.) with Dirichlet boundary conditions. We perturb A by some real valued potential V is an element of C-0(infinity) (Omega) and note A(V) = A + V. We compute the asymptotic expansion of tr(e-(tAV)-e(-tA)) as t down arrow 0 for any matrix a with constant coefficients. In the particular case where A is the Dirichlet Laplacian in Omega, that is when a is the identity of R-n2, we make the four main terms appearing in the asymptotic expansion formula explicit and prove that L-infinity-bounded sets of isospectral potentials of A are bounded in H-2(Omega). |
Year | DOI | Venue |
|---|---|---|
2015 | 10.3233/ASY-141277 | ASYMPTOTIC ANALYSIS |
Keywords | Field | DocType |
heat trace asymptotics,isospectral potentials | Nabla symbol,Isospectral,Mathematical analysis,Sobolev space,Dirichlet boundary condition,Asymptotic expansion,Dirichlet distribution,Asymptotic analysis,Mathematics,Laplace operator | Journal |
Volume | Issue | ISSN |
92 | 3-4 | 0921-7134 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mourad Choulli | 1 | 0 | 1.01 |
| Laurent Kayser | 2 | 0 | 0.34 |
| Yavar Kian | 3 | 0 | 1.01 |
| Eric Soccorsi | 4 | 0 | 1.69 |