Uniqueness and Nonuniqueness in Inverse Problems for Elliptic Partial Differential Equations and Related Medical Imaging by Kiwoon Kwon

“…Unique determination issues about inverse problems for elliptic partial differential equations in divergence form are summarized and discussed. …”
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An experimental comparison of two preconditioned iterative methods to solve the elliptic partial differential equations by Seyyed Ahmad Edalatpanah

“…This paper aims to investigate an experimental comparison between two kinds of iterative models for solving the elliptic partial differential equations. Different tools of solution such as stationary and non-stationary iterative methods with preconditioning models have been studied. …”
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An Lp-Estimate for Weak Solutions of Elliptic Equations by Sara Monsurrò, Maria Transirico

“…We prove an Lp-a priori bound, p>2, for solutions of second order linear elliptic partial differential equations in divergence form with discontinuous coefficients in unbounded domains.…”
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Degenerate Differential Operators with Parameters by Veli B. Shakhmurov

“…In applications, the nonlocal boundary value problems for degenerate elliptic partial differential equations and for systems of elliptic equations with parameters on cylindrical domain are studied.…”
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Some maximum principles for solutions of a class of partial differential equations in Ω⊂ℝn by Mohammad Mujalli Al-Mahameed

“…We find maximum principles for solutions of semilinear elliptic partial differential equations of the forms: (1) Δ2u+αf(u)=0, α∈ℝ+ and (2) ΔΔu+α(Δu)k+gu=0, α≤0 in some region Ω⊂ℝn.…”
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Local estimates for functionals rotationally invariant with respect to the gradient by Telma João Santos

“…Inspired by properties associated with results which are valid for elliptic partial differential equations, it presents some local estimates nearby non extremum points as well as nearby extremum points for these problems, generalizing some results obtained by Arrigo Cellina, Vladimir V. …”
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W2,p-Solvability of the Dirichlet Problem for Elliptic Equations with Singular Data by Loredana Caso, Roberta D’Ambrosio, Maria Transirico

“…We give an overview on some results concerning the unique solvability of the Dirichlet problem in W2,p, p>1, for second-order linear elliptic partial differential equations in nondivergence form and with singular data in weighted Sobolev spaces. …”
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Maximal regular boundary value problems in Banach-valued function spaces and applications by Veli B. Shakhmurov

“…In applications, the nonlocal boundary value problems for quasi elliptic partial differential equations, nonlocal initial boundary value problems for parabolic equations, and their systems on cylindrical domain are studied.…”
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Numerical Solution of Poisson's Equation Using a Combination of Logarithmic and Multiquadric Radial Basis Function Networks by Mohammad Mehdi Mazarei, Azim Aminataei

“…This paper presents numerical solution of elliptic partial differential equations (Poisson's equation) using a combination of logarithmic and multiquadric radial basis function networks. …”
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A novel computational analysis of boundary-driven two-dimensional heat flow with internal heat generation by Muhammad Abid, Madiha Bibi, Nasir Yasin, Muhammad Shahid

“…Accurate numerical solution of parabolic and elliptic partial differential equations governing two-dimensional heat transfer is critical for engineering simulations but computationally challenging.This work employs key numerical techniques finite differences, conjugate gradients, and Crank-Nicolson time stepping to solve the heat diffusion equation and analyze method performance.The Poisson equation is discretized using second-order central finite differences and solved with the conjugate gradient approach to determine the steady state solution. …”
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Finite Volume Element Approximation for the Elliptic Equation with Distributed Control by Quanxiang Wang, Tengjin Zhao, Zhiyue Zhang

“…In this paper, we consider a priori error estimates for the finite volume element schemes of optimal control problems, which are governed by linear elliptic partial differential equation. The variational discretization approach is used to deal with the control. …”
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Optimal investment game for two regulated players with regime switching by Lin Xu, Linlin Wang, Hao Wang, Liming Zhang

“…In the first case, the associated Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation was an elliptic partial differential equation (PDE). By solving an auxiliary problem, we demonstrated the existence and regularity of the value function. …”
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