In this paper,we study the p-Laplacian equation of the form−Δ_(p)u+h(x)|u|^(p−2)u=(R_(α)∗|u|^(q))|u|^(q−2)u+|u|^(2q−2)u on lattice graphs Z^(N),where N∈N^(∗),α∈(0,N),2≤p<2Nq/N+α<+∞and and R_(α)represent...In this paper,we study the p-Laplacian equation of the form−Δ_(p)u+h(x)|u|^(p−2)u=(R_(α)∗|u|^(q))|u|^(q−2)u+|u|^(2q−2)u on lattice graphs Z^(N),where N∈N^(∗),α∈(0,N),2≤p<2Nq/N+α<+∞and and R_(α)represents the Green’s function of the discrete fractional Laplacian,which has no singularity at the origin but behaves as the Riesz potential at infinity.Under suitable assumptions on the potential h(x),we prove the existence of ground state solutions to the equation above by two different methods.展开更多
In this paper, we first introduce interpolation operator of projection type in three dimen- sions, from which we derive weak estimates for tricubic block finite elements. Then using the estimate for the W 2, 1-seminor...In this paper, we first introduce interpolation operator of projection type in three dimen- sions, from which we derive weak estimates for tricubic block finite elements. Then using the estimate for the W 2, 1-seminorm of the discrete derivative Green's function and the weak estimates, we show that the tricubic block finite element solution uh and the tricubic interpolant of projection type Πh3u have superclose gradient in the pointwise sense of the L∞-norm. Finally, this supercloseness is applied to superconvergence analysis, and the global superconvergence of the finite element approximation is derived.展开更多
For a general second-order variable coefficient elliptic boundary value problem in three dimensions, the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements. In add...For a general second-order variable coefficient elliptic boundary value problem in three dimensions, the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements. In addition, the estimate for the W1,1-seminorm of the discrete derivative Green＇s function is given. Finally, the authors show that the derivatives of the finite element solution uh and the corresponding interpolant Hu are superclose in the pointwise sense of the L∞-norm.展开更多
文摘In this paper,we study the p-Laplacian equation of the form−Δ_(p)u+h(x)|u|^(p−2)u=(R_(α)∗|u|^(q))|u|^(q−2)u+|u|^(2q−2)u on lattice graphs Z^(N),where N∈N^(∗),α∈(0,N),2≤p<2Nq/N+α<+∞and and R_(α)represents the Green’s function of the discrete fractional Laplacian,which has no singularity at the origin but behaves as the Riesz potential at infinity.Under suitable assumptions on the potential h(x),we prove the existence of ground state solutions to the equation above by two different methods.
基金supported by Natural Science Foundation of Ningbo City (Grant No. 2008A610020)National Natural Science Foundation of China (Grant No. 10671065)the Scientific Research Fund of Hunan Provincial Education Department (Grant Nos. 07C576, 03C212)
文摘In this paper, we first introduce interpolation operator of projection type in three dimen- sions, from which we derive weak estimates for tricubic block finite elements. Then using the estimate for the W 2, 1-seminorm of the discrete derivative Green's function and the weak estimates, we show that the tricubic block finite element solution uh and the tricubic interpolant of projection type Πh3u have superclose gradient in the pointwise sense of the L∞-norm. Finally, this supercloseness is applied to superconvergence analysis, and the global superconvergence of the finite element approximation is derived.
基金supported by the Natural Science Foundation of Zhejiang Province under Grant No.Y6090131the Natural Science Foundation of Ningbo City under Grant No.2010A610101
文摘For a general second-order variable coefficient elliptic boundary value problem in three dimensions, the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements. In addition, the estimate for the W1,1-seminorm of the discrete derivative Green＇s function is given. Finally, the authors show that the derivatives of the finite element solution uh and the corresponding interpolant Hu are superclose in the pointwise sense of the L∞-norm.
