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pro vyhledávání: '"35j15"'
Autor:
Perelmuter, M. A.
We give $L^p$ estimates for the second derivatives of weak solutions to the Dirichlet problem for equation $\Div(\mathbf{A}\nabla u) = f$ in $\Omega\subset \mathbb{R}^d$ with Sobolev coefficients. In particular, for $f\in L^2(\Omega) \bigcap L^s(\Ome
Externí odkaz:
http://arxiv.org/abs/2411.09378
Autor:
George, Mathew
A complex Monge-Amp\`ere equation for differential $(p,p)$ forms is introduced on compact K\"ahler manifolds. For any $1 \leq p < n$, we show the existence of smooth solutions unique up to adding constants. For $p=1$, this corresponds to the Calabi-Y
Externí odkaz:
http://arxiv.org/abs/2411.06497
Autor:
Cavallina, Lorenzo
This paper investigates the solutions to the two-phase Serrin's problem, an overdetermined boundary value problem motivated by shape optimization. Specifically, we study the torsional rigidity of composite beams, where two distinct materials interact
Externí odkaz:
http://arxiv.org/abs/2411.00320
We propose some general growth conditions on the function $% f=f\left( x,\xi \right) $, including the so-called natural growth, or polynomial, or $p,q-$growth conditions, or even exponential growth, in order to obtain that any local minimizer of the
Externí odkaz:
http://arxiv.org/abs/2410.22875
Autor:
Han, Bin, Michelle, Michelle
This paper introduces a wavelet Galerkin method for solving two-dimensional elliptic interface problems of the form in $-\nabla\cdot(a\nabla u)=f$ in $\Omega\backslash \Gamma$, where $\Gamma$ is a smooth interface within $\Omega$. The variable scalar
Externí odkaz:
http://arxiv.org/abs/2410.16596
Autor:
Calamai, Alessandro, Infante, Gennaro
We investigate the existence of nontrivial solutions of parameter-dependent elliptic equations with deviated argument in annular-like domains in $\mathbb{R}^{n}$, with $n\geq 2$, subject to functional boundary conditions. In particular we consider a
Externí odkaz:
http://arxiv.org/abs/2410.11615
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