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In this paper, we study the shape optimization problem for the first eigenvalue of the $p$-Laplace operator with the mixed Neumann-Dirichlet boundary conditions on multiply-connected domains in hyperbolic space. Precisely, we establish that…

In this note we generalize the main result in [DIV: R. Di Gennaro, G. Ilardi, J. Valles, Singular hypersurfaces characterizing the Lefschetz properties J. Lond. Math. Soc. (2) 89 (2014), no. 1, 194-212] on artinian ideals failing Lefschetz…

G-splines are a generalization of B-splines that deals with extraordinary points by imposing G^1 constraints across their spoke edges, thus obtaining a continuous tangent plane throughout the surface. Using the isoparametric concept and the…

Given a star-shaped bounded Lipschitz domain $\Omega\subset{\mathbb R}^d$, we consider the Schr\"odinger operator $L_{\mathcal G}=-\Delta+V$ on $\Omega$ and its restrictions $L^{\Omega_t}_{\mathcal G}$ on the subdomains $\Omega_t$,…

In this paper we present an iterative method, inspired by the inverse iteration with shift technique of finite linear algebra, designed to find the eigenvalues and eigenfunctions of the Laplacian with homogeneous Dirichlet boundary…

We consider the optimal arrangement of two diffusion materials in a bounded open set $\Omega\subset \mathbb{R}^N$ in order to maximize the energy. The diffusion problem is modeled by the $p$-Laplacian operator. It is well known that this…

This study presents novel strategies for improving the node-level performance of matrix-free evaluation of continuous and discontinuous Galerkin spatial discretizations on unstructured tetrahedral grids. In our approach the underlying…

A family of optimal control problems for a single and two coupled spinning particles in the Euler-Lagrange formalism is discussed. A characteristic of such problems is that the equations controlling the system are implicit and a reduction…

We prove generalized Gaffney inequalities and the discrete compactness for finite element differential forms on $s$-regular domains, including general Lipschitz domains. In computational electromagnetism, special cases of these results have…

An approach to the construction of index formulas for elliptic operators on singular manifolds is suggested on the basis of K-theory of algebras and cyclic cohomology. The equivalence of Toeplitz and pseudodifferential quantizations, well…

This paper studies nonlinear eigenvalues problems with a double non homogeneity governed by the $p(x)$-Laplacian operator, under the Dirichlet boundary condition on a bounded domain of $\mathbb{R}^N(N\geq2)$. According to the type of the…

It is well-known that the finite difference discretization of the Laplacian eigenvalue problem $-\Delta u = \lambda u$ leads to a matrix eigenvalue problem (EVP) $A x= \lambda x$ where the matrix $A$ is Toeplitz-plus-Hankel. Analytical…

A matrix $A$ is said to have $X$-simple image eigenspace if any eigenvector $x$ belonging to the interval $X=\{x\colon \underline{x}\leq x\leq\overline{x}\}$ is the unique solution of the system $A\otimes y=x$ in $X$. The main result of…

We develop eigenvalue estimates for the Laplacians on discrete and metric graphs using different types of boundary conditions at the vertices of the metric graph. Via an explicit correspondence of the equilateral metric and discrete graph…

Efficient solution of the lowest eigenmodes is studied for a family of related eigenvalue problems with common $2\times 2$ block structure. It is assumed that the upper diagonal block varies between different versions while the lower…

We prove sharp bounds on eigenvalues of the Laplacian that complement the Faber--Krahn and Luttinger inequalities. In particular, we prove that the ball maximizes the first eigenvalue and minimizes the spectral zeta function and heat trace.…

Adapting the method of Andrews-Clutterbuck we prove an eigenvalue gap theorem for a class of non symmetric second order linear elliptic operators on a convex domain in euclidean space. The class of operators includes the Bakry-Emery…

We consider a nonlinear eigenvalue problem for some elliptic equations governed by general operators including the $p$-Laplacian. The natural framework in which we consider such equations is that of Orlicz-Sobolev spaces. we exhibit two…

In this paper we provide a priori error estimates in standard Sobolev (semi-)norms for approximation in spline spaces of maximal smoothness on arbitrary grids. The error estimates are expressed in terms of a power of the maximal grid…

We consider the Shallow Water equations in the supercritical and subcritical cases in one space variable,posed in a finite spatial interval with characteristic boundary conditions at the endpoints, which, as is well known, are…