Taiwanese Journal of Mathematics

ON THE REGULARITY OF SOLUTION OF THE SECOND INITIAL BOUNDARY VALUE PROBLEM FOR SCHRÖDINGER SYSTEMS IN DOMAINS WITH CONICAL POINTS

Nguyen Manh Hung and Nguyen Thi Kim Son

Full-text: Open access

Abstract

Some results on the unique solvability and the regularity of solution of the second initial boundary value problem for strongly Schrödinger systems in finite and infinite cylinders with the bases containing conical points are given.

Article information

Source
Taiwanese J. Math., Volume 13, Number 6B (2009), 1885-1907.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405647

Digital Object Identifier
doi:10.11650/twjm/1500405647

Mathematical Reviews number (MathSciNet)
MR2583527

Zentralblatt MATH identifier
1195.35113

Subjects
Primary: 35D05 35D10 35G99: None of the above, but in this section

Keywords
second initial boundary value problem Schrödinger systems generalized solution existence uniqueness smoothness regularity

Citation

Hung, Nguyen Manh; Son, Nguyen Thi Kim. ON THE REGULARITY OF SOLUTION OF THE SECOND INITIAL BOUNDARY VALUE PROBLEM FOR SCHRÖDINGER SYSTEMS IN DOMAINS WITH CONICAL POINTS. Taiwanese J. Math. 13 (2009), no. 6B, 1885--1907. doi:10.11650/twjm/1500405647. https://projecteuclid.org/euclid.twjm/1500405647


Export citation

References

  • R. A. Adams, Sobolev Spaces, Academic Press, 1975.
  • E. V. Frolova, An initial boundary-value problem with a noncoercive boundary condition in domains with edges, Zap. Nauchn. Semis. LOMI, 188 (1994), 206-223.
  • N. M. Hung, The first initial boundary value problem for Schrödinger systems in non-smooth domains, Diff. Urav., 34 (1998), pp. 1546-1556 (in Russian).
  • N. M. Hung and C. T. Anh, On the solvability of the first initial boundary value problem for Schrödinger systems in infinite cylinders, Vietnam J. Math., 32(1) (2004), pp. 41-48.
  • N. M. Hung and C. T. Anh, On the smoothness of solutions of the first initial boundary value problem for Schrödinger systems in domains with conical points, Vietnam J. Math., 32(2) (2005), pp. 135-147.
  • A. Kokotov and B. Plamenevsky, On the asymptotics on solutions to the Neumann problem for hyperbolic systems in domains with conical points, OAlgebra i analiz, 16 (2004) (in Russian), English transl., St. Peterburg Math. J., 16 (2005), N$^\circ$ 3, pp. 477-506.
  • V. A. Kondratiev, Boundary value problems for elliphic equations in domains with conical or angular points, Trudy Moskov. Mat. Obshch, 16 (1967), 209-292, (in Russian).
  • O. A. Ladyzhenskaya, On the non-stationary operator equations and its application to linear problems of Mathematical Physics, Mat. Sbornik., 45(87) (1958) 123-158 (in Russian).
  • V. G. Mazýa, V. A. Kozlov and J. Rossmann, Elliptic boundary value problems in domains with point singularities, Mathematical Surveys and Monographs 52, Amer. Math. Soc., Provodence, Rhode Island, 1997.
  • V. G. Mazýa and B. A. Plamenevsky, On the coefficients in the asymptotic of solutions to the elliptic boundary value problems in domains with conical points, Math. Nachr., 76 (1977), 29-60.
  • L. Nirenberg, Remarks on strongly elliptic partial differential equations, Communications on pure and applied mathematics, Vol 8, 1955, pp. 648-674.
  • V. A. Solonnikov, On the solvability of classical initial-boundary value problem for the heat equation in a dihedral angle, Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst., 127 (1983), 7-48.