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pro vyhledávání: '"Nitsch, C."'
By means of a suitable weighted rearrangement, we obtain various apriori bounds for the solutions to a Robin problem. Among other things, we derive a family of Faber-Krahn type inequalities.
Externí odkaz:
http://arxiv.org/abs/2207.14010
Artificial Neuronal Networks are models widely used for many scientific tasks. One of the well-known field of application is the approximation of high-dimensional problems via Deep Learning. In the present paper we investigate the Deep Learning techn
Externí odkaz:
http://arxiv.org/abs/2110.02112
We show, using symmetrization techniques, that it is possible to prove a comparison principle (we are mainly focused on $L^1$ comparison) between solutions to an elliptic partial differential equation on a smooth bounded set $\Omega$ with a rather ge
Externí odkaz:
http://arxiv.org/abs/2009.04320
Akademický článek
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Comparison results of Talenti type for Elliptic Problems with Dirichlet boundary conditions have been widely investigated in the last decades. In this paper, we deal with Robin boundary conditions. Surprisingly, contrary to the Dirichlet case, Robin
Externí odkaz:
http://arxiv.org/abs/1909.11950
Let $\Omega$ be an open convex set in ${\mathbb R}^m$ with finite width, and let $v_{\Omega}$ be the torsion function for $\Omega$, i.e. the solution of $-\Delta v=1, v\in H_0^1(\Omega)$. An upper bound is obtained for the product of $\Vert v_{\Omega
Externí odkaz:
http://arxiv.org/abs/1811.04503
In this paper we prove that the ball maximizes the first eigenvalue of the Robin Laplacian operator with negative boundary parameter, among all convex sets of \mathbb{R}^n with prescribed perimeter. The key of the proof is a dearrangement procedure o
Externí odkaz:
http://arxiv.org/abs/1810.06108
Autor:
Nitsch, C., Trombetti, C.
In this survey we consider the classical overdetermined problem which was studied by Serrin in 1971. The original proof relies on Alexandrov's moving plane method, maximum principles, and a refinement of Hopf's boundary point Lemma. Since then other
Externí odkaz:
http://arxiv.org/abs/1711.10787
Autor:
Arling, J. -H., Gerhardt, M., Gößling, C., Gehre, D., Klingenberg, R., Kröninger, K., Nitsch, C., Quante, T., Rohatsch, K., Tebrügge, J., Temminghoff, R., Theinert, R., Zatschler, S., Zuber, K.
Publikováno v:
J.-H. Arling et al 2017 JINST 12 P11025
The COBRA collaboration searches for neutrinoless double beta-decay ($0\nu\beta\beta$-decay) using CdZnTe semiconductor detectors with a coplanar-grid readout and a surrounding guard-ring structure. The operation of the COBRA demonstrator at the Gran
Externí odkaz:
http://arxiv.org/abs/1701.07432
In this short note we consider an unconventional overdetermined problem for the torsion function: let $n\geq 2$ and $\Omega$ be a bounded open set in $\mathbb{R}^n$ whose torsion function $u$ (i.e. the solution to $\Delta u=-1$ in $\Omega$, vanishing
Externí odkaz:
http://arxiv.org/abs/1701.05821