Some New A Priori Estimates for Second-Order Elliptic and Parabolic Interface Problems

Abstract We present some new a priori estimates of the solutions to the second-order elliptic and parabolic interface problems. The novelty of these estimates lies in the explicit appearance of the discontinuous coefficients and the jumps of coefficients across the interface.

[1]  G. Hedstrom,et al.  Numerical Solution of Partial Differential Equations , 1966 .

[2]  J. Lions.  Quelques méthodes de résolution de problèmes aux limites non linéaires , 2017 .

[3]  R. B. Kellogg,et al.  SINGULARITIES IN INTERFACE PROBLEMS , 1971 .

[4]  J. Lions,et al.  Non-homogeneous boundary value problems and applications , 1972 .

[5]  A. Aziz.  The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations , 1972 .

[6]  R. Kellogg.  HIGHER ORDER SINGULARITIES FOR INTERFACE PROBLEMS , 1972 .

[7]  Joseph J. Kohn,et al.  Pseudo-di erential operators and hypoellipticity , 1973 .

[8]  R. Bruce Kellogg,et al.  On the poisson equation with intersecting interfaces , 1974 .

[9]  Michael Taylor,et al.  Pseudo differential operators , 1974 .

[10]  Jacques Chazarain,et al.  Introduction to the theory of linear partial differential equations , 1982 .

[11]  G. Verchota.  Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains , 1984 .

[12]  P. Grisvard.  Elliptic Problems in Nonsmooth Domains , 1985 .

[13]  Michael Taylor,et al.  Pseudodifferential Operators and Nonlinear PDE , 1991 .

[14]  Luis Escauriaza,et al.  On a regularity theorem for weak solutions to transmission problems with internal Lipschitz boundaries , 1992 .

[15]  Jianxin Zhou,et al.  Boundary element methods , 1992, Computational mathematics and applications.

[16]  J. Retherford,et al.  Hilbert Space: Compact Operators and the Trace Theorem , 1993 .

[17]  R. LeVeque,et al.  A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources , 2006 .

[18]  Carlos E. Kenig,et al.  Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems , 1994 .

[19]  Jin Keun Seo,et al.  The layer potential technique for the inverse conductivity problem , 1996 .

[20]  J. Seo,et al.  Numerical identification of discontinuous conductivity coefficients , 1997 .

[21]  L. Ying.  INTERFACE PROBLEMS FOR ELLIPTIC DIFFERENTIAL EQUATIONS , 1997 .

[22]  Y. Meyer,et al.  Wavelets: Calderón-Zygmund and Multilinear Operators , 1997 .

[23]  J. Zou,et al.  Finite element methods and their convergence for elliptic and parabolic interface problems , 1998 .

[24]  Jinchao Xu,et al.  Some Nonoverlapping Domain Decomposition Methods , 1998, SIAM Rev..

[25]  Zhilin Li.  The immersed interface method using a finite element formulation , 1998 .

[26]  Michael Taylor,et al.  Tools for Pde: Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials , 2000 .

[27]  Jun Zou,et al.  A mortar element method for elliptic problems with discontinuous coefficients , 2002 .

[28]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.