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Regularity of solutions of initial-boundary value problems for parabolic equations in domains with conical points. (English) Zbl 1170.35048
Summary: The purpose of this paper is to establish the well-posedness and the regularity of solutions of the initial-boundary value problems for general higher order parabolic equations in infinite cylinders with the bases containing conical points.
##### MSC:
 35K35 Higher order parabolic equations, boundary value problems 35B65 Smoothness and regularity of solutions of PDE 35K25 Higher order parabolic equations, general 35D10 Regularity of generalized solutions of PDE (MSC2000)
##### References:
 [1] Evans, L. C.: Partial differential equations, Grad stud. Math. 19 (1998) · Zbl 0902.35002 [2] Frolova, E. V.: An initial boundary value problem with a noncoercive boundary condition in domains with edges, Zap. nauchn. Sem. LOMI 188, 206-223 (1994) · Zbl 0867.35038 [3] Kondrat’ev, V. A.; Oleinik, O. A.: Boundary value problems for partial differential equations in nonsmooth domains, Uspekhi mat. Nauk 38, No. 3(230), 3-76 (1983) · Zbl 0523.35010 [4] Kozlov, V. A.; Maz’ya, V. G.; Rossmann, J.: Elliptic boundary problems in domains with point singularities, Math. surveys monogr. 52 (1997) · Zbl 0947.35004 [5] Kozlov, V. A.; Maz’ya, V. G.; Rossmann, J.: Spectral problems associated with corner singularities of solutions to elliptic equations, Math. surveys monogr. 85 (2001) · Zbl 0965.35003 [6] N.M. Hung, Boundary problems for nonstationary systems in domains with a nonsmooth boundary, Doctor dissertation, Mech. Math. Department MSU, Moscow, 1999 [7] Hung, N. M.; Duong, P. T.: On the smoothness of generalized solution for parabolic systems in domains with conic points on boundary, Ukrainian math. J. 56, No. 6, 857-864 (2004) · Zbl 1142.35447 [8] Ladyzhenskaya, O. A.; Solonnikov, V. A.; Uraltseva, N. N.: Linear and quasilinear equations of parabolic type, (1967) · Zbl 0164.12302 [9] Maz’ya, V. G.; Plamenevskii, B. A.: Lp estimates of solutions of elliptic boundary value problems in domains with edges, Tr. mosk. Mat. obs. 37, 49-93 (1978) [10] Rossmann, J.: The asymptotics of the solutions of elliptic variational problems in domains with edges on the boundary, Z. angew. Math. mech. 9, No. 3, 565-575 (1990) · Zbl 0725.49002 [11] Solonnikov, V. A.: On the solvability of classical initial – boundary value problem for the heat equation in a dihedral angle, Zap. nauchn. Sem. leningr. Otdel. mat. 127, 7-48 (1983)