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A Weak Galerkin Finite Element Method for $p$-Laplacian Problem

East Asian Journal on Applied Mathematics, 2021
In this paper, we introduce a weak Galerkin (WG) finite element method for p-Laplacian problem on general polytopal mesh. The quasi-optimal error estimates of the weak Galerkin finite element approximation are obtained. The numerical examples confirm the
Xiuxiu Zhang
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Optimal Error Estimates of a Linearized Crank-Nicolson Galerkin FEM for the Kuramoto-Tsuzuki Equations

Communications in Computational Physics, 2019
This paper is concerned with unconditionally optimal error estimate of the linearized Galerkin finite element method for solving the two-dimensional and threedimensional Kuramoto-Tsuzuki equations, while the classical analysis for these nonlinear ...
Dongfang Li
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Removable singularities for elliptic equations with $(p,q)$-growth conditions

Differential and Integral Equations, 2018
For solutions of a class of divergence type quasilinear elliptic equations with (p, q)-growth conditions we establish the condition for removability of singularity on manifolds. 1991 Mathematics Subject Classification. 35B45, 35J60.
Yuliya V. Namlyeyeva, I. Skrypnik
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A Remark on the Level Sets of the Graph of Harmonic Functions Bounded by Two Circles in Parallel Planes

, 2015
In this paper, we find two auxiliary functions and make use of the maximum principle to study the level sets of harmonic function defined on a convex ring with homogeneous Dirichlet boundary conditions in R2.
Kong, Shengli, Xu, Jinju
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W2,p-Regularity of Lp Viscosity Solutions to Fully Nonlinear Elliptic Equations with Low-Order Terms

Journal of Advances in Applied & Computational Mathematics
In this paper, we consider the following fully nonlinear elliptic equation                                                                      F(D2u, Du, x) = f(x), where the operator F satisfies structure condition and the gradient of solution has ...
Shuhan Hao, Yao Zhang, Zhenqiu Zhang
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Second Order Estimates for Non-concave Hessian Type Elliptic Equations on Riemannian Manifolds

, 2015
In this paper, we derive second order estimates for a class of non-concave Hessian type elliptic equations on Riemannian manifolds. By applying a new method for C2 estimates, we can weaken some conditions, which works for some non-concave equations ...
H. Jiao
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