- Volume 19 Issue 2
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.
- Gilbarg, D.; Trudinger, N. S. Elliptic partial differential equations of second order. Reprint of the 1998 ed. Springer-Verlag, Berlin, 2001.
- 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
- 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.
- Ladyzhenskaya, O. A.; Solonnikov, V. A.; Ural'tseva, N. N. Linear and quasilinear equations of parabolic type. American Mathematical Society: Providence, RI, 1967.
- Lieberman G. M. Second order parabolic differential equations, World Scientific Publishing Co., Inc., River Edge, NJ, 1996.
- DiBenedetto, E. Partial differential equations. Second edition. Birkhauser Boston, Inc., Boston, MA, 2010.
- 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