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NOTE ON LOCAL BOUNDEDNESS FOR WEAK SOLUTIONS OF NEUMANN PROBLEM FOR SECOND-ORDER ELLIPTIC EQUATIONS

  • KIM, SEICK (DEPARTMENT OF MATHEMATICS, YONSEI UNIVERSITY)
  • Received : 2015.04.20
  • Accepted : 2015.05.16
  • Published : 2015.06.25

Abstract

The goal of this note is to provide a detailed proof for local boundedness estimate near the boundary for weak solutions for second order elliptic equations with bounded measurable coefficients subject to Neumann boundary condition.

References

  1. Gilbarg, D.; Trudinger, N. S. Elliptic partial differential equations of second order. Reprint of the 1998 ed. Springer-Verlag, Berlin, 2001.
  2. Choi, J.; Kim, S. Neumann functions for second order elliptic systems with measurable coefficients. Trans. Amer. Math. Soc. 365 (2013), no. 12, 6283-6307. https://doi.org/10.1090/S0002-9947-2013-05886-2
  3. Ladyzhenskaya, O. A.; Ural'tseva, N. N. Linear and quasilinear elliptic equations. Translated from the Russian by Scripta Technica, Inc. Academic Press, New York-London, 1968.
  4. Ladyzhenskaya, O. A.; Solonnikov, V. A.; Ural'tseva, N. N. Linear and quasilinear equations of parabolic type. American Mathematical Society: Providence, RI, 1967.
  5. Lieberman G. M. Second order parabolic differential equations, World Scientific Publishing Co., Inc., River Edge, NJ, 1996.
  6. DiBenedetto, E. Partial differential equations. Second edition. Birkhauser Boston, Inc., Boston, MA, 2010.

Cited by

  1. NOTE ON LOCAL ESTIMATES FOR WEAK SOLUTION OF BOUNDARY VALUE PROBLEM FOR SECOND ORDER PARABOLIC EQUATION vol.53, pp.4, 2016, https://doi.org/10.4134/BKMS.b150567