Related papers: A remark on partial data inverse problems for semi…

We study various partial data inverse boundary value problems for the semilinear elliptic equation $\Delta u+ a(x,u)=0$ in a domain in $\mathbb R^n$ by using the higher order linearization technique introduced in [LLS 19, FO19]. We show…

Given a conformally transversally anisotropic manifold $(M,g)$, we consider the semilinear elliptic equation $$(-\Delta_{g}+V)u+qu^2=0\quad \text{on $M$}.$$ We show that an a priori unknown smooth function $q$ can be uniquely determined…

In this paper, we study the partial data inverse problem for nonlinear magnetic Schr\"odinger equations. We show that the knowledge of the Dirichlet-to-Neumann map, measured on an arbitrary part of the boundary, determines the…

The Dirichlet problem and Dirichlet to Neumann map are analyzed for elliptic equations on a large collection of infinite quantum graphs. For a dense set of continuous functions on the graph boundary, the Dirichlet to Neumann map has values…

We show that a general nonlinearity $a(x,u)$ is uniquely determined, possibly up to a gauge, in a neighborhood of a fixed solution from boundary measurements of the corresponding semilinear equation. The main theorems are low regularity…

We investigate the monotonicity method for fractional semilinear elliptic equations with power type nonlinearities. We prove that if-and-only-if monotonicity relations between coefficients and the derivative of the Dirichlet-to-Neumann map…

This paper studies an inverse boundary value problem for a semilinear Helmholtz equation with Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ ($n\ge2$). The objective is to recover the unknown linear and…

We study the well-posedness of a semilinear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map.…

A large class of initial-boundary value problems of linear evolution partial differential equations formulated on the half-line is analyzed via the unified transform method. In particular, explicit formulae are presented for the generalized…

We study the inverse problem of identifying a periodic potential perturbation of the Dirichlet Laplacian acting in an infinite cylindrical domain, whose cross section is assumed to be bounded. We prove log-log stable determination of the…

In this paper, we prove that there exists a unique solution to the Dirichlet boundary value problem for a general class of semilinear second order elliptic partial differential equations. Our approach is probabilistic. The theory of…

This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main…

Some linear integro-differential operators have old and classical representations as the Dirichlet-to-Neumann operators for linear elliptic equations, such as the 1/2-Laplacian or the generator of the boundary process of a reflected…

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…

We consider the Dirichlet problem for semilinear elliptic equations on a bounded domain which is diffeomorphic to a ball and investigate bifurcation from a given (trivial) branch of solutions, where the radius of the ball serves as…

We study a nonlinear elliptic boundary value problem defined on a smooth bounded domain involving the fractional Laplace operator, a concave-convex powers term together with mixed Dirichlet-Neumann boundary conditions.

We study the inverse problem of determining uniquely and stably quasilinear terms appearing in an elliptic equation from boundary excitations and measurements associated with the solutions of the corresponding equation. More precisely, we…

We show that the knowledge of the Dirichlet--to--Neumann map for a nonlinear magnetic Schr\"odinger operator on the boundary of a compact complex manifold, equipped with a K\"ahler metric and admitting sufficiently many global holomorphic…

We study a semilinear elliptic problem with a singular nonlinear term of the type $g(u)=-u^{-1}$, using a variational approach. Note that the minus sign is important since the corresponding term in the Euler-Lagrange functional is concave.…

We show that if $u$ is a solution to a linear elliptic differential equation of order $2m\geq 2$ in the half-space with $t$-independent coefficients, and if $u$ satisfies certain area integral estimates, then the Dirichlet and Neumann…