Related papers: Nonlinear elliptic eigenvalue problems in cylindri…
We consider singular perturbed eigenvalue problem for Laplace operator in a two-dimensional domain. In the boundary we select a set depending on a character small parameter and consisting of a great number of small disjoint parts. On this…
This paper deals with a class of singularly perturbed nonlinear elliptic problems $(P_\e)$ with subcritical nonlinearity. The coefficient of the linear part is assumed to concentrate in a point of the domain, as $\e\to 0$, and the domain is…
This paper consists of two parts. In the first part, which is of more abstract nature, the notion of quasi boundary triples and associated Weyl functions is developed further in such a way that it can be applied to elliptic boundary value…
We derive the asymptotic expansion at infinity for embedded ends of uniformly elliptic Weingarten surfaces with finite total curvature in $\mathbb{R}^3$, and we establish a maximum principle at infinity. Furthermore, we solve the Dirichlet…
In this work we study the asymptotic distribution of eigenvalues in one-dimensional open sets. The method of proof is rather elementary, based on the Dirichlet lattice points problem, which enable us to consider sets with infinite measure.…
We consider elliptic equations in planar domains with mixed boundary conditions of Dirichlet-Neumann type. Sharp asymptotic expansions of the solutions and unique continuation properties from the Dirichlet-Neumann junction are proved.
In this work we apply the unfolding operator method to analyze the asymptotic behavior of the solutions of the $p$-Laplacian equation with Neumann boundary condition set in a bounded thin domain of the type…
In this paper, we study an eigenvalue problem with piecewise constant coefficients on thin domains with Neumann boundary condition, and we analyze the asymptotic behavior of each eigenvalue as the domain degenerates into a certain…
In this paper, we want to study the asymptotic behavior of the first $p$-Laplacian eigenvalue, with Robin boundary conditions, with negative boundary parameter. In particular, we prove that the limit of the eigenfunctions is a viscosity…
This article focuses on Lp-estimates for the square root of elliptic systems of second order in divergence form on a bounded domain. We treat complex bounded measurable coefficients and allow for mixed Dirichlet/Neumann boundary conditions…
The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in smooth three-dimensional domains is characterized by model problems inside the domain or on its boundary.…
We consider second order elliptic operators with real, nonsymmetric coefficient functions which are subject to mixed boundary conditions. The aim of this paper is to provide uniform resolvent estimates for the realizations of these…
This thesis is concerned with the asymptotic behavior of solutions of stochastic $p$-Laplace equations driven by non-autonomous forcing on $\mathbb{R}^n$. Two cases are studied, with additive and multiplicative noise respectively. Estimates…
We consider a thin multidomain of $R^N$, N>1, consisting of two vertical cylinders, one placed upon the other: the first one with given height and small cross section, the second one with small thickness and given cross section. In this…
We review recent advances in solving problems of mathematical physics on domains with irregular boundaries in Rn. We distinguish two frameworks: a measure-free approach in the image of the trace operator spaces for extension domains and an…
In this paper, we establish the well-posedness and large-time asymptotic behavior of viscosity solutions to singular/degenerate parabolic $p$-Laplacian equations with general capillary-type boundary conditions, including Neumann and…
For a second order formally symmetric elliptic differential expression we show that the knowledge of the Dirichlet-to-Neumann map or Robin-to-Dirichlet map for suitably many energies on an arbitrarily small open subset of the boundary…
This paper investigates the asymptotic behavior of a class of nonlinear variational problems with Robin-type boundary conditions on a bounded Lipschitz domain. The energy functional contains a bulk term (the $p$-norm of the gradient), a…
In this paper we are concerned with the initial boundary value problems of linear and semi-linear parabolic equations with mixed boundary conditions on non-cylindrical domains in spatial-temporal space. We obtain the existence of a weak…
In this paper, we explore the geometric properties of unbounded extremal domains for the $p$-Laplacian operator in both Euclidean and hyperbolic spaces. Assuming that the nonlinearity grows at least as the nonlinearity of the eigenvalue…