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The operator of double differentiation on a finite interval with Robin boundary conditions perturbed by the composition of a Volterra convolution operator and the differentiation one is considered. We study the inverse problem of recovering…

Spectral Theory · Mathematics 2020-01-28 S. A. Buterin , A. E. Choque Rivero

The challenge of solving the initial value problem for the coupled Lakshmanan Porsezian Daniel equation, while considering nonzero boundary conditions at infinity, is addressed through the development of a suitable inverse scattering…

Exactly Solvable and Integrable Systems · Physics 2024-04-05 Peng-Fei Han , Ru-Suo Ye , Yi Zhang

In this work, the Dirac-type integro di{\S}erential system with one classical boundary condition and another nonlocal integral boundary condition is considered. We obtain the asymptotic formulae for the solutions, eigenvalues and nodal…

Spectral Theory · Mathematics 2022-03-25 Baki Keskin

In this paper we consider a Robin-type Laplace operator on bounded domains. We study the dependence of its lowest eigenvalue on the boundary conditions and its asymptotic behavior in shrinking and expanding domains. For convex domains we…

Mathematical Physics · Physics 2012-12-18 Hynek Kovarik

The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on…

Numerical Analysis · Mathematics 2026-02-12 Sabia Asghar , Qiyao Peng , Fred Vermolen , Cornelis Vuik

We consider a family of initial boundary value problems governed by a fractional diffusion equation with Caputo derivative in time, where the parameter is the Newton heat transfer coefficient linked to the Robin condition on the boundary.…

Analysis of PDEs · Mathematics 2021-05-06 Isolda Cardoso , Sabrina D. Roscani , Domingo A. Tarzia

This paper is concerned with the Dirichlet eigenvalue problem for Laplace operator in a bounded domain with periodic perforation in the case of small volume. We obtain the optimal quantitative error estimates independent of the spectral…

Analysis of PDEs · Mathematics 2024-08-27 Zhongwei Shen , Jinping Zhuge

We consider an inverse boundary value problem for the Maxwell's equations with a given data assumed to be known only in accessible part $\Gamma$ of the boundary. We aim to prove an uniqueness result using the Dirichlet to Neumann map with…

Mathematical Physics · Physics 2020-07-14 Christian Daveau , Abdessatar Khelifi , Houssem Lihiou

In this paper, we study a class of eigenvalue problems involving both local as well as nonlocal operators, precisely the classical Laplace operator and the fractional Laplace operator in the presence of mixed boundary conditions, that is…

Analysis of PDEs · Mathematics 2024-11-26 Jacques Giacomoni , Tuhina Mukherjee , Lovelesh Sharma

We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a…

Analysis of PDEs · Mathematics 2020-04-15 Isaac Harris , Andreas Kleefeld

Let $\Delta_{\Lambda}\le \lambda_{\Lambda}$ be a semi-bounded self-adjoint realization of the Laplace operator with boundary conditions (Dirichlet, Neumann, semi-transparent) assigned on the Lipschitz boundary of a bounded obstacle…

Analysis of PDEs · Mathematics 2020-06-15 Andrea Mantile , Andrea Posilicano

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…

Geophysics · Physics 2012-05-29 Nick Polydorides , Alireza Aghasi , Eric L. Miller

We give a counterexample to the long standing conjecture that the ball maximises the first eigenvalue of the Robin eigenvalue problem with negative parameter among domains of the same volume. Furthermore, we show that the conjecture holds…

Spectral Theory · Mathematics 2015-07-31 Pedro Freitas , David Krejcirik

We prove the existence of a principal eigenvalue associated to the $\infty$-Laplacian plus lower order terms and the Neumann boundary condition in a bounded smooth domain. As an application we get uniqueness and existence results for the…

Analysis of PDEs · Mathematics 2008-06-03 Stefania Patrizi

Lieb has shown a lower bound on the smallest Dirichlet eigenvalue of the Laplace operator in terms of a generalized inradius. We derive similar bounds for Robin eigenvalues, for eigenvalues of the polyharmonic operator and the sub-Laplacian…

Spectral Theory · Mathematics 2025-09-24 Rupert L. Frank , Ari Laptev , Durvudkhan Suragan

This paper deals with the Sturm-Liouville problem that feature distribution potential, polynomial dependence on the spectral parameter in the first boundary condition, and analytical dependence, in the second one. We study an inverse…

Spectral Theory · Mathematics 2024-09-05 E. E. Chitorkin , N. P. Bondarenko

In this paper, further to the point interaction method for inverse Sturm-Liouville problems on finite intervals firstly proposed in our previous work, we will continue to generalize this method to the inverse eigenvalue problems for…

Classical Analysis and ODEs · Mathematics 2025-10-13 Min Zhao , Jiangang Qi , Xiao Chen

We consider uniqueness in an inverse Schr\"odinger problem in a bounded domain in $\mathbb{R}^2$ given the Dirichlet-to-Neumann map on part of the boundary. On the remaining boundary we impose a new type of singular boundary condition with…

Analysis of PDEs · Mathematics 2018-09-19 Freddy J. F. Symons

In this paper, we consider a problem for the first order Dirac differential equations system with spectral parameter dependent in boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this…

Spectral Theory · Mathematics 2014-04-02 Kh. R. Mamedov , O. Akcay

Let $\Omega$ be a bounded and smooth domain of $\mathbb{R}^{N}$, $N\geq2$, and consider the eigenvalue problem: $-\Delta_{p}u=\lambda\left| u\right| _{L^{q}(\Omega)}^{p-q}\left| u\right| ^{q-2}u$ in $\Omega,$ $u=0$ on $\partial\Omega,$…

Analysis of PDEs · Mathematics 2017-08-03 Grey Ercole