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pro vyhledávání: '"35J70"'
Autor:
Long, Bingsong
We consider two-dimensional Riemann boundary value problems of Euler equations for the Chaplygin gas with two piecewise constant initial data outside a convex cornered wedge. In self-similar coordinates, when the flow at the wedge corner is subsonic,
Externí odkaz:
http://arxiv.org/abs/2411.06108
We establish interior $W^{2,\delta}$ type estimates for a class of degenerate fully nonlinear elliptic equations with $L^n$ data. The main idea of our approach is to slide $C^{1,\alpha}$ cones, instead of paraboloids, vertically to touch the solution
Externí odkaz:
http://arxiv.org/abs/2411.02846
Autor:
Delande, Loïs
We consider the Witten Laplacian associated to a non-Morse potential. We prove Eyring-Kramers formulas for the bottom of the spectrum of this operator in the semiclassical regime and quantify the spectral gap between these eigenvalues and the rest of
Externí odkaz:
http://arxiv.org/abs/2410.21899
Autor:
Giovagnoli, Davide, Jesus, David
In this paper we prove that solutions to a transmission problem degenerating on the interface are H\"older differentiable up to the interface with universal estimates. Furthermore, we obtain a sharper pointwise $C^{1,\alpha(\cdot)}$ with optimal vari
Externí odkaz:
http://arxiv.org/abs/2410.16957
Autor:
Eisenhuth, Benedikt, Grothaus, Martin
We consider a degenerate infinite dimensional stochastic Hamiltonian system with multiplicative noise and establish the essential m-dissipativity on $L^2(\mu^{\Phi})$ of the corresponding Kolmogorov (backwards) operator. Here, $\Phi$ is the potential
Externí odkaz:
http://arxiv.org/abs/2410.15993
The Grushin Laplacian $- \Delta_\alpha $ is a degenerate elliptic operator in $\mathbb{R}^{h+k}$ that degenerates on $\{0\} \times \mathbb{R}^k$. We consider weak solutions of $- \Delta_\alpha u= Vu$ in an open bounded connected domain $\Omega$ with
Externí odkaz:
http://arxiv.org/abs/2410.12637
We introduce and analyse a class of weighted Sobolev spaces with mixed weights on angular domains. The weights are based on both the distance to the boundary and the distance to the one vertex of the domain. Moreover, we show how the regularity of th
Externí odkaz:
http://arxiv.org/abs/2409.18615
In this paper, we deal with the following $(p,q)$-fractional problem $$ (-\Delta)^{s_{1}}_{p}u +(-\Delta)^{s_{2}}_{q}u=\lambda P(x)|u|^{k-2}u+\theta|u|^{p_{s_{1}}^{*}-2}u \, \mbox{ in }\, \Omega,\qquad u=0\, \mbox{ in }\, \mathbb{R}^{N} \setminus \Om
Externí odkaz:
http://arxiv.org/abs/2409.13986
Autor:
da Silva, Genival
We discuss the existence and regularity of solutions to the following Dirichlet problem: $$\begin{equation} \begin{cases} -\textrm{div}\left(\frac{Du}{(1+|u|)^{\theta}}\right)= -\textrm{div}\left(u^{\gamma}E(x)\right)+f(x) \qquad & \mbox{in } \Omega,
Externí odkaz:
http://arxiv.org/abs/2409.13182
We introduce fractional weighted Sobolev spaces with degenerate weights. For these spaces we provide embeddings and Poincar\'e inequalities. When the order of fractional differentiability goes to $0$ or $1$, we recover the weighted Lebesgue and Sobol
Externí odkaz:
http://arxiv.org/abs/2409.11829