Results 1 to 10 of about 6,239,552 (226)

The Dirichlet Problem of Hessian Equation in Exterior Domains [PDF]

Mathematics, 2020
In this paper, we will obtain the existence of viscosity solutions to the exterior Dirichlet problem for Hessian equations with prescribed asymptotic behavior at infinity by the Perron’s method. This extends the Ju–Bao results on Monge–Ampère equations
Hongfei Li, Limei Dai
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The exterior Dirichlet problem for the homogeneous complex k-Hessian equation

Advanced Nonlinear Studies, 2023
In this article, we consider the homogeneous complex kk-Hessian equation in an exterior domain Cn⧹Ω{{\mathbb{C}}}^{n}\setminus \Omega . We prove the existence and uniqueness of the C1,1{C}^{1,1} solution by constructing approximating solutions.
Gao Zhenghuan, Ma Xinan, Zhang Dekai
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A Perturbed Cauchy Viscoelastic Problem in an Exterior Domain [PDF]

Mathematics, 2023
A Cauchy viscoelastic problem perturbed by an inverse-square potential, and posed in an exterior domain of RN, is considered under a Dirichlet boundary condition.
Bessem Samet, Calogero Vetro
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The Dirichlet Problem for the Equation Δu−k2u=0 in the Exterior of Nonclosed Lipschitz Surfaces

International Journal of Mathematics and Mathematical Sciences, 2013
We study the Dirichlet problem for the equation Δu−k2u=0 in the exterior of nonclosed Lipschitz surfaces in R3. The Dirichlet problem for the Laplace equation is a particular case of our problem. Theorems on existence and uniqueness of a weak solution of
P. A. Krutitskii
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The exterior Dirichlet problems of Monge–Ampère equations in dimension two [PDF]

Boundary Value Problems, 2020
In this paper, we study the Monge–Ampère equations det D 2 u = f $\det D^{2}u=f$ in dimension two with f being a perturbation of f 0 $f_{0}$ at infinity.
Limei Dai
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Asymptotics and Uniqueness of Solutions of the Elasticity System with the Mixed Dirichlet–Robin Boundary Conditions

Mathematics, 2020
We study properties of generalized solutions of the Dirichlet–Robin problem for an elasticity system in the exterior of a compact, as well as the asymptotic behavior of solutions of this mixed problem at infinity, with the condition that the energy ...
Hovik A. Matevossian
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Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations

Boundary Value Problems, 2022
In this paper, we consider the exterior Dirichlet problem of Hessian equations σ k ( λ ( D 2 u ) ) = g ( x ) $\sigma _{k}(\lambda (D^{2}u))=g(x)$ with g being a perturbation of a general positive function at infinity. By estimating the eigenvalues of the
Limei Dai, Hongfei Li
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Parabolic Hessian Equations Outside a Cylinder

Mathematics, 2022
In this article, we mainly review the parabolic Hessian equation on the exterior region. The existence and uniqueness of solutions with asymptotic properties to the exterior problem of the parabolic Hessian equation were obtained by using the Perron ...
Limei Dai, Xuewen Guo
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On the Solvability of the Generalized Neumann Problem for a Higher-Order Elliptic Equation in an Infinite Domain

Современная математика: Фундаментальные направления, 2021
We consider the generalized Neumann problem for a 2lth-order elliptic equation with constant real higher-order coefficients in an infinite domain containing the exterior of some circle and bounded by a sufficiently smooth contour.
B. D. Koshanov, A. P. Soldatov
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On the Wiener criterion in higher dimensions

Boundary Value Problems, 2017
The Wiener criterion is a sufficient and necessary condition for the solvability of the Dirichlet problem. However, its geometric interpretation is not clear.
Tariq Ismaeel
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