Related papers: Nonhomogeneous boundary condition for spectral non…

In this paper, we present a problem involving fully nonlinear elliptic operators with Hamiltonian, which can present a singularity or degenerate as the gradient approaches the origin. The model studied here, allows the appearance of plateau…

We study integral operators $\mathcal{L}u(x)=\int_{\mathbb{R^N}}\psi(u(x)-u(y))J(x-y)\,dy$ of the type of the fractional $p$-Laplacian operator, and the properties of the corresponding Orlicz and Sobolev-Orlicz spaces. In particular we show…

We consider the homogenization of a singularly perturbed self-adjoint fourth order elliptic equation with locally periodic coefficients, stated in a bounded domain. We impose Dirichlet boundary conditions on the boundary of the domain. The…

In this paper, we investigate the existence of weak solution for a fractional type problems driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions. We first extend…

Initial-boundary value problems for integrable nonlinear partial differential equations have become tractable in recent years due to the development of so-called unified transform techniques. The main obstruction to applying these methods…

A bosonic Laplacian is a conformally invariant second order differential operator acting on smooth functions defined on domains in Euclidean space and taking values in higher order irreducible representations of the special orthogonal…

In this paper, the asymptotic behavior of the solutions of a monotone problem posed in a locally periodic oscillating domain is studied. Nonlinear monotone boundary conditions are imposed on the oscillating part of the boundary whereas the…

We analyze an approximation of a Laplacian subject to non-local interface conditions of a $\delta'$-type by Neumann Laplacians on a family of Riemannian manifolds with a sieve-like structure. We establish a (kind of) resolvent convergence…

A nonuniform Neumann boundary-value problem is considered for the Poisson equation in a thin domain $\Omega_\varepsilon$ coinciding with two thin rectangles connected through a joint of diameter ${\cal O}(\varepsilon)$. A rigorous procedure…

We consider elliptic equations and systems in divergence form with the conormal or the Robin boundary conditions, with small BMO (bounded mean oscillation) or variably partially small BMO coefficients. We propose a new class of domains…

Let $L$ be a second order uniformly elliptic differential operator in a domain $D$ of $\mathbb{R}^{d}$, $\psi:\mathbb{R}_+\to \mathbb{R}_+$ be a nondecreasing continuous function and let $\xi,g:D\to\mathbb{R}_+$ be locally bounded Borel…

We consider a nonlinear elliptic equation driven by a nonhomogeneous differential operator plus an indefinite potential. On the reaction term we impose conditions only near zero. Using variational methods, together with truncation and…

Let $\Omega\subset\BBR^N$ be a bounded $C^2$ domain and $\CL_\gk=-\Gd-\frac{\gk}{d^2}$ the Hardy operator where $d=\dist (.,\prt\Gw)$ and $0<\gk\leq\frac{1}{4}$. Let $\ga_{\pm}=1\pm\sqrt{1-4\gk}$ be the two Hardy exponents, $\gl_\gk$ the…

We consider self-adjoint extensions of differential operators of the type $ (-\frac{d^2}{dr^2} + \frac{l(l+1)}{r^2})^3 $ on the real semi-axis for l=1,2 with two kinds of boundary conditions: first that nullify the value of a function and…

We study the Laplace operator on the Sierpinski gasket with nonlinear Robin boundary conditions. We show that for certain Robin boundary conditions the Laplace operator generates a positive, order preserving, $L^\infty$-contractive…

We study half-line Schr\"odinger operators with locally $H^{-1}$ potentials. In the first part, we focus on a general spectral theoretic framework for such operators, including a Last--Simon-type description of the absolutely continuous…

The purpose of this paper is to investigate the existence of three different weak solutions to a nonlinear elliptic problem that is governed by the weighted {\varphi}-Laplacian operator and subjected to Dirichlet boundary conditions. We…

This work introduces efficient and accurate spectral solvers for nonlocal equations on bounded domains. These spectral solvers exploit the fact that integration in the nonlocal formulation transforms into multiplication in Fourier space and…

The Cahn--Hilliard equation is one of the most common models to describe phase segregation processes in binary mixtures. In recent times, various dynamic boundary conditions have been introduced to model interactions of the materials with…

We consider a stochastic boundary value elliptic problem on a bounded domain $D\subset \mathbb{R}^k$, driven by a fractional Brownian field with Hurst parameter $H=(H_1,...,H_k)\in[{1/2},1[^k$. First we define the stochastic convolution…