In this paper we prove that isometries with respect to the Kobayashi metric between certain domains having boundary points at which the boundary is infinitely flat extend continuously to the boundary.The strategy is t...In this paper we prove that isometries with respect to the Kobayashi metric between certain domains having boundary points at which the boundary is infinitely flat extend continuously to the boundary.The strategy is to reestablish the Gehring-Hayman-type Theorem for these complex domains.Furthermore,the regularity of boundary extension map is given.展开更多
A new boundary extension technique based on the Lagrange interpolat- ing polynomial is proposed and used to solve the function approximation defined on an interval by a series of scaling Coiflet functions, where the c...A new boundary extension technique based on the Lagrange interpolat- ing polynomial is proposed and used to solve the function approximation defined on an interval by a series of scaling Coiflet functions, where the coefficients are used as the single-point samplings. The obtained approximation formula can exactly represent any polynomials defined on the interval with the order up to one third of the length of the compact support of the adopted Coiflet function. Based on the Galerkin method, a Coifiet-based solution procedure is established for general two-dimensional p^Laplacian equations, following which the equations can be discretized into a concise matrix form. As examples of applications, the proposed modified wavelet Galerkin method is applied to three typical p-Laplacian equations with strong nonlinearity. The numerical results justify the efficiency and accuracy of the method.展开更多
基金supported by National Key R&D Program of China(Grant No.2021YFA1003100)NSFC(Grant Nos.11925107 and 12226334)+2 种基金Key Research Program of Frontier Sciences,CAS(Grant No.ZDBS-LY-7002)supported by the Young Scientist Program of the Ministry of Science and Technology of China(Grant No.2021YFA1002200)NSFC(Grant No.12201059)。
文摘In this paper we prove that isometries with respect to the Kobayashi metric between certain domains having boundary points at which the boundary is infinitely flat extend continuously to the boundary.The strategy is to reestablish the Gehring-Hayman-type Theorem for these complex domains.Furthermore,the regularity of boundary extension map is given.
基金supported by the National Natural Science Foundation of China(Nos.11472119 and11421062)
文摘A new boundary extension technique based on the Lagrange interpolat- ing polynomial is proposed and used to solve the function approximation defined on an interval by a series of scaling Coiflet functions, where the coefficients are used as the single-point samplings. The obtained approximation formula can exactly represent any polynomials defined on the interval with the order up to one third of the length of the compact support of the adopted Coiflet function. Based on the Galerkin method, a Coifiet-based solution procedure is established for general two-dimensional p^Laplacian equations, following which the equations can be discretized into a concise matrix form. As examples of applications, the proposed modified wavelet Galerkin method is applied to three typical p-Laplacian equations with strong nonlinearity. The numerical results justify the efficiency and accuracy of the method.
