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pro vyhledávání: '"35j15"'
Autor:
Schino, Jacopo, Smyrnelis, Panayotis
Given $m \in \mathbb{N} \setminus \{0\}$ and $\rho > 0$, we find solutions $(\lambda,u)$ to the problem \begin{equation*} \begin{cases} \bigl(-\frac{\mathrm{d}^2}{\mathrm{d} x^2}\bigr)^m u + \lambda G'(u) = F'(u)\\ \int_{\mathbb{R}} K(u) \, \mathrm{d
Externí odkaz:
http://arxiv.org/abs/2410.03318
Autor:
Boutillon, Nathanaël
We consider a nonlocal Fisher-KPP equation that models a population structured in space and in phenotype. The population lives in a heterogeneous periodic environment: the diffusion coefficient, the mutation coefficient and the fitness of an individu
Externí odkaz:
http://arxiv.org/abs/2410.01342
Autor:
Boutillon, Nathanaël, Rossi, Luca
We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenotypic trait may be more or less fit according to the spatial location.
Externí odkaz:
http://arxiv.org/abs/2409.20118
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
Autor:
Marcati, Carlo, Schwab, Christoph
We study the approximation rates of a class of deep neural network approximations of operators, which arise as data-to-solution maps $\mathcal{G}^\dagger$ of linear elliptic partial differential equations (PDEs), and act between pairs $X,Y$ of suitab
Externí odkaz:
http://arxiv.org/abs/2409.17552
Motivated by the study of the electrodynamics of particles, we propose in this work an arbitrary-order discrete de Rham scheme for the treatment of elliptic problems with potential and flux jumps across a fixed interface. The scheme seamlessly suppor
Externí odkaz:
http://arxiv.org/abs/2409.15042
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 propose and rigorously analyze a finite element method for the approximation of stationary Fokker--Planck--Kolmogorov (FPK) equations subject to periodic boundary conditions in two settings: one with weakly differentiable coefficients, and one wit
Externí odkaz:
http://arxiv.org/abs/2409.07371
Autor:
Dong, Hongjie, Wang, Ming
It is well known that every solution of an elliptic equation is analytic if its coefficients are analytic. However, less is known about the ultra-analyticity of such solutions. This work addresses the problem of elliptic equations with lower-order te
Externí odkaz:
http://arxiv.org/abs/2409.07027
Autor:
Jung, Pilgyu, Woo, Kwan
We explore the higher integrability of Green's functions associated with the second-order elliptic equation $a^{ij}D_{ij}u + b^i D_iu = f$ in a bounded domain $\Omega \subset \mathbb{R}^d$, and establish a version of Aleksandrov's maximum principle.
Externí odkaz:
http://arxiv.org/abs/2408.16522