Related papers: On a quasilinear mean field equation with exponent…

We study an elliptic equation, with homogeneous Dirichlet boundary conditions, driven by a mixed type operator (the sum of the Laplacian and the fractional Laplacian), involving a parametric reaction and an undetermined source term.…

A simple approach is proposed for the quantization of the electromagnetic field in nonlinear and inhomogeneous media. Given the dielectric function and nonlinear susceptibilities, the Hamiltonian of the electromagnetic field is determined…

In this article, we study the impact of a change in the type of boundary conditions of an elliptic boundary value problem. In the context of the conductivity equation we consider a reference problem with mixed homogeneous Dirichlet and…

We consider the Cauchy problem for non-autonomous forms inducing elliptic operators in divergence form with Dirichlet, Neumann, or mixed boundary conditions on an open subset $\Omega$ $\subseteq$ R n. We obtain maximal regularity in L 2…

We consider a nonlinear eigenvalue problem under Robin boundary conditions in a domain with (possibly noncompact) smooth boundary. The problem involves a weighted p-Laplacian operator and subcritical nonlinearities satisfying…

We consider the Lane-Emden equation with a supercritical nonlinearity with an inhomogeneous Dirichlet boundary condition on an infinite cone. Under suitable conditions for the boundary data and the exponent of nonlinearity, we give a…

If $({\cal E}, {\cal D})$ is a symmetric, regular, strongly local Dirichlet form on $L^2 (X,m)$, admitting a carr\'{e} du champ operator $\Gamma$, and $p>1$ is a real number, then one can define a nonlinear form ${\cal E}^p$ by the formula…

In this article we study the behavior as $p \nearrow+\infty$ of the Fucik spectrum for $p$-Laplace operator with zero Dirichlet boundary conditions in a bounded domain $\Omega\subset \mathbb{R}^n$. We characterize the limit equation, and we…

We consider a general second order linear elliptic equation in a finely perforated domain. The shapes of cavities and their distribution in the domain are arbitrary and non-periodic; they are supposed to satisfy minimal natural geometric…

It is widely known that the spectrum of the Dirichlet Laplacian is stable under small perturbations of a domain, while in the case of the Neumann or mixed boundary conditions the spectrum may abruptly change. In this work we discuss an…

The non-relativistic Schr\"odinger equation on a domain $\Omega\subset \mathbb{R}^d$ with boundary is often considered with homogeneous Dirichlet boundary conditions ($\psi(x)=0$ for $x$ on the boundary), homogeneous Neumann boundary…

We study the $\bar{\partial}_b$-Neumann problem for domains $\Omega$ contained in a strictly pseudoconvex manifold M^{2n+1} whose boundaries are noncharacteristic and have defining functions depending solely on the real and imaginary parts…

We study the problem of imposing Dirichlet-like boundary conditions along a static spatial curve, in a planar Noncommutative Quantum Field Theory model. After constructing interaction terms that impose the boundary conditions, we discuss…

For an open, bounded domain $\Om$ in $\mathbb{R}^N$ which is strictly convex with $C^2$ boundary, we show that there exists a $\land>0$ such that the singular quasilinear problem \begin{eqnarray*} &-\delp u…

In this paper we deal with the following question: is it true that any bounded smooth pseudoconvex domain in $\mathbb{C}^n$ whose boundary contains a $q$-dimensional complex manifold $M$ necessarily has a noncompact…

We study some Dirichlet problem for a $p$--Laplacian type operator in the setting of Orlicz--Zygmund space $L^q\log^{-\alpha}L(\Omega,\mathbb R^N)$, $q >1$ and $\alpha>0$. More precisely, our aim is to establish which assuptions on the…

In this work we analyze convergence of solutions for the Laplace operator with Neumann boundary conditions in a two-dimensional highly oscillating domain which degenerates into a segment (thin domains) of the real line. We consider the case…

In this paper we study, in an open bounded set $\Omega\subset\mathbb R^N$ with Lipschitz boundary $\partial\Omega$, the Dirichlet problem for a nonlinear singular elliptic equation involving the $1$--Laplacian and a total variation term,…

In this work we consider the asymptotic behavior of the nonlinear semigroup defined by a semilinear parabolic problem with homogeneous Neumann boundary conditions posed in a bounded region of the plane that degenerates into a line segment…

A Bernoulli free boundary problem with geometrical constraints is studied. The domain $\Om$ is constrained to lie in the half space determined by $x_1\geq 0$ and its boundary to contain a segment of the hyperplane $\{x_1=0\}$ where…