Zobrazeno 1 - 10
of 1 398
pro vyhledávání: '"Rose, Christian"'
Autor:
Keller, Matthias, Rose, Christian
We investigate the equivalence of Sobolev inequalities and the conjunction of Gaussian upper heat kernel bounds and volume doubling on large scales on graphs. For the normalizing measure, we obtain their equivalence up to constants by imposing compar
Externí odkaz:
http://arxiv.org/abs/2406.19879
Autor:
Rose, Christian, Nichols, Taylor, Hackner, Daniel, Chang, Julia, Straube, Steven, Jooste, Willem, Sawe, Hendry, Tenner, Andrea
Publikováno v:
JMIR Formative Research, Vol 5, Iss 5, p e14851 (2021)
BackgroundHealth systems in low- and middle-income countries face considerable challenges in providing high-quality accessible care. eHealth has had mounting interest as a possible solution given the unprecedented growth in mobile phone and internet
Externí odkaz:
https://doaj.org/article/ae80c72c6c284f398d5486612ad777ec
Autor:
Rose, Christian, Tautenhahn, Martin
We prove quantitative unique continuation estimates for relatively dense sets and spectral subspaces associated to small energies of Schr\"odinger operators on Riemannian manifolds with Ricci curvature bounded below. The upper bound for the energy ra
Externí odkaz:
http://arxiv.org/abs/2305.06916
Autor:
Keller, Matthias, Rose, Christian
We derive Gaussian heat kernel bounds on graphs with respect to a fixed origin for large times under the assumption of a Sobolev inequality and volume doubling on large balls. The upper bound from our previous work [KR22] is affected by a new correct
Externí odkaz:
http://arxiv.org/abs/2212.11722
Autor:
Keller, Matthias, Rose, Christian
We prove large-time Gaussian upper bounds for continuous-time heat kernels of Laplacians on graphs with unbounded geometry. Our estimates hold for centers of large balls satisfying a Sobolev inequality and volume doubling. Distances are measured with
Externí odkaz:
http://arxiv.org/abs/2206.04690
We obtain a fundamental gap estimate for classes of bounded domains with quantitative control on the boundary in a complete manifold with integral bounds on the negative part of the Ricci curvature. This extends the result of \cite{Oden-Sung-Wang99}
Externí odkaz:
http://arxiv.org/abs/2109.11181
Publikováno v:
J. Differential Equations 369 (2023), 405--423
Recent (scale-free) quantitative unique continuation estimates for spectral subspaces of Schr\"odinger operators are extended to allow singular potentials such as certain $L^p$-functions. The proof is based on accordingly adapted Carleman estimates.
Externí odkaz:
http://arxiv.org/abs/2011.01801