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In this article we investigate averaging properties of fully nonlinear PDEs in bounded domains with oscillatory Neumann boundary data. The oscillation is periodic and is present both in the operator and in the Neumann data. Our main result…

We study existence and uniqueness of solutions to a class of nonlinear degenerate parabolic equations, in bounded domains. We show that there exists a unique solution which satisfies possibly inhomogeneous Dirichlet boundary conditions. To…

In this paper, we consider an acoustic wave transmission problem with mixed boundary conditions of Dirichlet, Neumann, and impedance type. The transmission interfaces may join the domain boundary in a general way independent of the location…

In this paper, we consider the wave equation for the Laplace operator with potential, initial data, and nonhomogeneous Dirichlet boundary condition. We establish a weak solution by using traces and extension domains. We also establish the…

We consider a 2-dimensional thin domain with order of thickness {\epsilon} which presents oscillations of amplitude also {\epsilon} on both boundaries, top and bottom, but the period of the oscillations are of different order at the top and…

We present examples of isospectral operators that do not have the same heat content. Several of these examples are planar polygons that are isospectral for the Laplace operator with Dirichlet boundary conditions. These include examples with…

We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator with a growth of order $(p-1)$ near $+\infty$ and with a reaction which has the competing effects of a parametric singular term and a…

This work is devoted to the asymptotic behavior of eigenvalues of an elliptic operator with rapidly oscillating random coefficients on a bounded domain with Dirichlet boundary conditions. A sharp convergence rate is obtained for isolated…

We are concerned with inverse boundary problems for first order perturbations of the Laplacian, which arise as model operators in the acoustic tomography of a moving fluid. We show that the knowledge of the Dirichlet--to--Neumann map on the…

We consider the heat equation in a straight strip, subject to a combination of Dirichlet and Neumann boundary conditions. We show that a switch of the respective boundary conditions leads to an improvement of the decay rate of the heat…

We study Laplacians associated to a graph and single out a class of such operators with special regularity properties. In the case of locally finite graphs, this class consists of all selfadjoint, non-negative restrictions of the standard…

We consider the nonlinear eigenvalue problem, with Dirichlet boundary condition, for a class of very degenerate elliptic operators, with the aim to show that, at least for square type domains having fixed volume, the symmetry of the domain…

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…

We show that the fractional Laplacian can be viewed as a Dirichlet-to-Neumann map for a degenerate hyperbolic problem, namely, the wave equation with an additional diffusion term that blows up at time zero. A solution to this wave extension…

In this paper we study a bounded domain with a small hole removed. Our main result concerns the spectrum of the Laplace operator with the Robin conditions imposed at the hole boundary. Moreover we prove that under some suitable assumptions…

Let $T$ be a self-adjoint operator in a Hilbert space $H$ with domain $\mathcal D(T)$. Assume that the spectrum of $T$ is confined in the union of disjoint intervals $\Delta_k =[\alpha_{2k-1},\alpha_{2k}]$, $k\in \mathbb{Z}$, and $$…

We consider Laplacian in a straight planar strip with Dirichlet boundary which has two Neumann ``windows'' of the same length the centers of which are $2l$ apart, and study the asymptotic behaviour of the discrete spectrum as $l\to\infty$.…

We consider positive solutions, possibly unbounded, to the semilinear equation $-\Delta u=f(u)$ on continuous epigraphs bounded from below. Under the homogeneous Dirichlet boundary condition, we prove new monotonicity results for $u$, when…

We consider the spectral Dirichlet problem for the Laplace operator in the plane $\Omega^{\circ}$ with double-periodic perforation but also in the domain $\Omega^{\bullet}$ with a semi-infinite foreign inclusion so that the Floquet-Bloch…

In this paper we develop a Gidas-Ni-Nirenberg technique for polyharmonic equations and systems of Lane-Emden type. As far as we are concerned with Dirichlet boundary conditions, we prove uniqueness of solutions up to eighth order equations,…