Zobrazeno 1 - 10
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pro vyhledávání: '"Kriventsov, Dennis"'
We investigate general semilinear (obstacle-like) problems of the form $\Delta u = f(u)$, where $f(u)$ has a singularity/jump at $\{u=0\}$ giving rise to a free boundary. Unlike many works on such equations where $f$ is approximately homogeneous near
Externí odkaz:
http://arxiv.org/abs/2405.10418
Autor:
Kriventsov, Dennis, Soria-Carro, María
We study a two-phase parabolic free boundary problem motivated by the jump of conductivity in composite materials that undergo a phase transition. Each phase is governed by a heat equation with distinct thermal conductivity, and a transmission-type c
Externí odkaz:
http://arxiv.org/abs/2402.16805
Autor:
Kriventsov, Dennis, Li, Zongyuan
We prove three theorems about the asymptotic behavior of solutions $u$ to the homogeneous Dirichlet problem for the Laplace equation at boundary points with tangent cones. First, under very mild hypotheses, we show that the doubling index of $u$ eith
Externí odkaz:
http://arxiv.org/abs/2307.10517
Autor:
Kriventsov, Dennis, Weiss, Georg S.
While there are numerous results on minimizers or stable solutions of the Bernoulli problem proving regularity of the free boundary and analyzing singularities, much less in known about critical points of the corresponding energy. Saddle points of th
Externí odkaz:
http://arxiv.org/abs/2306.10131
We study the regularity of the interface between the disjoint supports of a pair of nonnegative subharmonic functions. The portion of the interface where the Alt-Caffarelli-Friedman (ACF) monotonicity formula is asymptotically positive forms an $\mat
Externí odkaz:
http://arxiv.org/abs/2210.03552
We study a Rayleigh-Faber-Krahn inequality for regional fractional Laplacian operators. In particular, we show that there exists a compactly supported nonnegative Sobolev function $u_0$ that attains the infimum (which will be a positive real number)
Externí odkaz:
http://arxiv.org/abs/2108.07967
For a domain $\Omega \subset \mathbb{R}^n$ and a small number $\frak{T} > 0$, let \[ \mathcal{E}_0(\Omega) = \lambda_1(\Omega) + {\frak{T}} {\text{tor}}(\Omega) = \inf_{u, w \in H^1_0(\Omega)\setminus \{0\}} \frac{\int |\nabla u|^2}{\int u^2} + {\fra
Externí odkaz:
http://arxiv.org/abs/2107.03495
Publikováno v:
Ars Inveniendi Analytica (2023), Paper No. 1, 49 pp
The objective of this paper is two-fold. First, we establish new sharp quantitative estimates for Faber-Krahn inequalities on simply connected space forms. We prove that the gap between the first eigenvalue of a given set $\Omega$ and that of the bal
Externí odkaz:
http://arxiv.org/abs/2107.03505
We prove a boundary Harnack principle in Lipschitz domains with small constant for fully nonlinear and $p$-Laplace type equations with a right hand side, as well as for the Laplace equation on nontangentially accessible domains under extra conditions
Externí odkaz:
http://arxiv.org/abs/2010.11854
We consider the semilinear problem \[ \Delta u = \lambda_+ \left(-\log u^+\right) 1_{\{u > 0\}} - \lambda_- \left(-\log u^- \right) 1_{\{u < 0\}} \qquad \hbox{ in } B_1, \] where $B_1$ is the unit ball in $\mathbb{R}^n$ and assume $\lambda_+, \lambda
Externí odkaz:
http://arxiv.org/abs/2009.03956