## Taiwanese Journal of Mathematics

### THE CAUCHY-NEUMANN PROBLEM FOR PARABOLIC EQUATIONS IN DOMAINS WITH CONICAL POINTS

#### Abstract

The purpose of this paper is to establish the well-posedness and the regularity of solutions of the Cauchy-Neumann problem for second order parabolic equations in cylinders with the base containing conical points.

#### Article information

Source
Taiwanese J. Math., Volume 12, Number 7 (2008), 1849-1864.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500405092

Digital Object Identifier
doi:10.11650/twjm/1500405092

Mathematical Reviews number (MathSciNet)
MR2449669

Zentralblatt MATH identifier
1172.35353

#### Citation

Hung, Nguyen Manh; Anh, Nguyen Thanh. THE CAUCHY-NEUMANN PROBLEM FOR PARABOLIC EQUATIONS IN DOMAINS WITH CONICAL POINTS. Taiwanese J. Math. 12 (2008), no. 7, 1849--1864. doi:10.11650/twjm/1500405092. https://projecteuclid.org/euclid.twjm/1500405092

#### References

• L. C. Evans, Partial differential equations, Graduate Studies in Mathematics Vol. 19, Amer. Math. Soc., Providence, Rhode Island 1998.
• V. A. Kondrat'ev and O. A. Oleinik, Boundary value problems for partial differential equations in nonsmooth domains (in Russian), Usp. Math. Nauka, 38(3) (1983), (230), 3-76.
• V. A. Kondrat'ev, On the smoothness of the solution of the Dirichlet of the second order in a piecewise-smooth domain, Diff. Urav. (in Russian), 6 (1970), 1831-1843.
• V. A. Kozlov, V. G. Maz'ya and J. Rossmann, Elliptic boundary problems in domains with point singularities, Mathematical Surveys and Monographs 85, Amer. Math. Soc., Providence, Rhode Island 1997.
• N. M. Hung and P. T. Duong, On the smoothness of generalized solution for parabolic systems in domains with conic points on boundary, Ucrain. Math. J., 56(6) (2004), 857-864.
• N. M. Hung and P. T. Duong, On the asymptotic behavior of generalized solution of parabolic systems in a neighborhood of conic point, ACTA Math. Viet., 30(2) (2004), 123-136.
• O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow, 1967.
• V. G. Maz'ya and B. A. Plamenevskii, $L_p$ estimates of solutions of elliptic boundary value problems in domains with edges, Trudy Moskov. Mat. Obshch., 37 (1978), 49-93; English transl. in: Trans. Moscow Math. Soc., 37 (1980), 49-97.
• 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. (in Russian), 127 (1983), 7-48.