Inverse problems for elliptic equations with power type nonlinearities
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In this article, a method for solving Calderon type inverse problems for semilinear equations with power type nonlinearities was introduced, which allows one to solve inverse problems in cases where the solution for a corresponding linear equation is not known.About:
This article is published in Journal de Mathématiques Pures et Appliquées.The article was published on 2021-01-01 and is currently open access. It has received 102 citations till now. The article focuses on the topics: Nonlinear system & Inverse problem.read more
Citations
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An inverse problem for a semi-linear elliptic equation in Riemannian geometries
Ali Feizmohammadi,Lauri Oksanen +1 more
TL;DR: In this paper, the authors studied the uniqueness of a complex-valued scalar function over a smooth compact Riemannian manifold with smooth boundary, given the Dirichlet-to-Neumann map, in a suitable sense, for the elliptic semi-linear equation − Δ g u + V (x, u ) = 0.
Journal ArticleDOI
Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities
Katya Krupchyk,Gunther Uhlmann +1 more
TL;DR: The linear span of the set of scalar products of gradients of harmonic functions on a bounded smooth domain which vanish on a closed proper subset of the boundary is dense in this paper.
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Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations
TL;DR: In this paper, the authors used the Dirichlet-to-Neumann map of the semilinear Schrodinger equation to solve the Calderon problem with partial data.
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Inverse problems for fractional semilinear elliptic equations
Ru-Yu Lai,Yi-Hsuan Lin +1 more
TL;DR: In this paper, the forward and inverse problems for the fractional semilinear elliptic equation were studied and the forward problem is well-posed and has a unique solution for small exterior data.
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A remark on partial data inverse problems for semilinear elliptic equations
Katya Krupchyk,Gunther Uhlmann +1 more
TL;DR: In this paper, it was shown that the knowledge of the Dirichlet-to-Neumann map on an arbitrary open portion of the boundary of a domain in O(n 2 ) for a class of semilinear elliptic equations determines the nonlinearity uniquely.
References
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Book
Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
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Elliptic Partial Differential Equations of Second Order
Piero Bassanini,Alan R. Elcrat +1 more
TL;DR: In this paper, a class of partial differential equations that generalize and are represented by Laplace's equation was studied. And the authors used the notation D i u, D ij u for partial derivatives with respect to x i and x i, x j and the summation convention on repeated indices.
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TL;DR: In this paper, a review of topology, linear algebra, algebraic geometry, and differential equations is presented, along with an overview of the de Rham Theorem and its application in calculus.
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Introduction to partial differential equations
TL;DR: The Introduction to Partial Differential Equations (IDEQE) as discussed by the authors is the most widely used partial differential equation (PDE) formalism for algebraic partial differential equations.