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On an Efficient Solution of the Dirichlet Problem for Properly Elliptic Equation in the Elliptic Domain
AbstractThe fourth-order properly elliptic equation with multiple root is considered in the elliptic domain. The conditions, necessary and sufficient...
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Boundary-Value Problem for Nonuniformly Elliptic Equations with Power Singularities
By using a priori estimates and the Riesz theorem, we investigate a boundary-value problem for nonuniformly 2 b -elliptic equations with arbitrary...
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Worked Out Problem 7: A Nonlinear Elliptic Problem
In this chapter, we consider a scalar nonlinear elliptic PDE as a benchmark for complex material problems in a two-dimensional domain. The aim is to...
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The Tricomi Problem for a Class of Multidimensional Hyperbolic-Elliptic Equations
AbstractThe solvability of the spatial Tricomi problem for a class of multidimensional hyperbolic-elliptic equations is proved.
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An Inverse Problem for a Quasilinear Elliptic Equation
We consider the inverse problem for a quasilinear second order elliptic equation with the unknown coefficient at the lower-order term and the first...
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Unique Solvability of the Zaremba Problem for Linear Second Order Elliptic Equations with Drift
We establish the unique solvability of the Zaremba problem for linear second order elliptic equations in divergence form with measurable coefficients...
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Iterative two-grid methods for discontinuous Galerkin finite element approximations of semilinear elliptic problem
In this paper, we design and analyze the iterative two-grid methods for the discontinuous Galerkin (DG) discretization of semilinear elliptic partial...
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On the Solvability of the Dirichlet Problem for a Multidimensional Elliptic System in the Half-Space
The Dirichlet problem for a multidimensional elliptic system in the half-space is considered. With the help of the Fourier transform, the problem of...
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The Dirichlet Problem for an Elliptic Equation with Three Singular Coefficients and Negative Parameters
We are interested in regular solutions to the first boundary value problem for a three-dimensional elliptic type equation with three singular...
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Worked Out Problem 16: A Parametrized Elliptic Optimal Control Problem
In this chapter, we consider a linear-quadratic optimal control problem with a vector elliptic PDE constraint in a two-dimensional and geometrically...
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An elliptic problem of the Prandtl–Batchelor type with a singularity
We establish the existence of at least two solutions of the Prandtl–Batchelor like elliptic problem driven by a power nonlinearity and a singular...
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Generalized Tikhonov regularization method for an inverse boundary value problem of the fractional elliptic equation
This research studies the inverse boundary value problem for fractional elliptic equation of Tricomi–Gellerstedt–Keldysh type and obtains a condition...
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Inverse Problem for Mixed-type Equation with an Elliptic Operator of Arbitrary Order
AbstractIn this paper, we consider the inverse problem of determining the source function for a mixed-type equation with a positive elliptic...
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Adaptive Finite Element Method for an Elliptic Optimal Control Problem with Integral State Constraints
In this article, we develop a posteriori error analysis of a nonconforming finite element method for a linear quadratic elliptic distributed optimal...
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Exterior Boundary-Value Poincaré Problem for Elliptic Systems of the Second Order with Two Independent Variables
This paper offers a number of examples showing that in the case of two independent variables the uniform ellipticity of a linear system of...
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Adaptive perturbation method for optimal control problem governed by stochastic elliptic PDEs
In this paper, we apply the stochastic perturbation technique to solve the optimal control problem governed by elliptic partial differential equation...
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Well-Posedness of the Generalized Samarskii–Ionkin Problem for Elliptic Equations in a Cylindrical Domain
AbstractWe study the well-posedness of some analogs of the nonlocal Samarskii–Ionkin problem for second-order elliptic equations in Sobolev spaces....
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On the Solvability of the Generalized Neumann Problem for a Higher-Order Elliptic Equation in an Infinite Domain
We consider the generalized Neumann problem for a 2 l th-order elliptic equation with constant real higher-order coefficients in an infinite domain...