Related papers: Nonlocal eigenvalue problems and superposition ope…
It is shown that eigenvalues of Laplace-Beltrami operators on compact Riemannian manifolds can be determined as limits of eigenvalues of certain finite-dimensional operators in spaces of polyharmonic functions with singularities. In…
We consider the eigenvalue problem for the Laplacian with mixed Dirichlet and Neumann boundary conditions. For a certain class of bounded, simply connected planar domains we prove monotonicity properties of the first eigenfunction. As a…
In this paper, we consider a nonlocal boundary-value problem for a mixed-type equation involving the bi-ordinal Hilfer fractional derivative in a rectangular domain. The main target of this work is to analyze the uniqueness and the…
Covering ill-posed problems with compact and non-compact operators regarding the degree of ill-posedness is a never ending story written by many authors in the inverse problems literature. This paper tries to add a new narrative and some…
We study a Dirichlet-to-Neumann eigenvalue problem for differential forms on a compact Riemannian manifold with smooth boundary. This problem is a natural generalization of the classical Steklov problem on functions. We derive a number of…
We prove some existence (and sometimes also uniqueness) of weak solutions to some stationary equations associated to the complex Schr\''{o}dinger operator under the presence of a singular nonlinear term. Among other new facts, with respect…
We investigate a perturbed Gelfand problem involving a mixed local-nonlocal $p$-Laplacian operator with singular nonlinearity: \begin{equation*} \begin{aligned} -\Delta_p u + (-\Delta_p)^s u = \lambda \frac{f(u)}{u^{\beta}}\ \text{in} \…
We extend the De Giorgi--Nash--Moser theory to superposition operators of mixed fractional operators. In particular, we investigate several regularity properties for this class of operators. We establish the Caccioppoli-type inequality with…
We investigate the qualitative properties of positive solutions to mixed local-nonlocal equations with indefinite nonlinearities, emphasizing the interaction between classical and fractional Laplacians. We first establish maximum principles…
We investigate a nonlinear nonlocal eigenvalue problem involving the sum of fractional $(p,q)$-Laplace operators $(-\Delta)_p^{s_1}+(-\Delta)_q^{s_2}$ with $s_1,s_2\in (0,1)$; $p,q\in(1,\infty)$ and subject to Dirichlet boundary conditions…
The purpose of this note is to review some recent results concerning the pseudospectra and the eigenvalues asymptotics of non-selfadjoint semiclassical pseudo-differential operators subject to small random perturbations.
In this paper, we consider an elliptic operator obtained as the superposition of a classical second-order differential operator and a nonlocal operator of fractional type. Though the methods that we develop are quite general, for…
In this paper we discuss reduced order models for the approximation of parametric eigenvalue problems. In particular, we are interested in the presence of intersections or clusters of eigenvalues. The singularities originating by these…
This paper is concerned with spectral estimates for the first Dirichlet eigenvalue of the degenerate $p$-Laplace operator in bounded simply connected domains $\Omega \subset \mathbb C$. The proposed approach relies on the conformal analysis…
In this paper we explore solvability of steady-state variational inequalities with multivalued operators. Moreover, we are studying the connections between the class of radially semi-continuous operators with semi-bounded variation and…
For a class of non-selfadjoint semiclassical operators in dimension one, we get a complete asymptotic description of all eigenvalues near a critical value of the leading symbol of the operator on the boundary of the pseudospectrum.
A third order self-adjoint differential operator with periodic boundary conditions and an one-dimensional perturbation has been considered. For this operator, we first show that the spectrum consists of simple eigenvalues and finitely many…
We consider a restricted Dirichlet-to-Neumann map associated to a wave type operator on a Riemannian manifold with boundary. The restriction corresponds to the case where the Dirichlet traces are supported on one subset of the boundary and…
We start in this paper a systematic study of the superpositions of elliptic operators with different orders, mixing classical and fractional scenarios. For concreteness, we focus on the sum of the Laplacian and the fractional Laplacian, and…
Recent literature on delocalization in non-Hermitian systems has stressed criteria based on sensitivity of eigenvalues to boundary conditions and the existence of a non-zero current. We emphasize here that delocalization also shows up…