Shizuta, Yasushi; Tanaka, Yumi Trace theorem in a class of anisotropic Sobolev spaces. (English) Zbl 0956.46026 Proc. Japan Acad., Ser. A 76, No. 3, 27-30 (2000). Authors’ abstract: A trace theorem and several lemmas for a class of anisotropic Sobolev spaces are given. These results are used to study the initial boundary value problem for symmetric hyperbolic systems with characteristic boundary of constant multiplicity. Especially, the trace theorem is needed for showing the necessity of the compatibility condition for the existence of solution to the characteristic mixed problem mentioned above. Reviewer: Josef Wloka (Kiel) MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems Keywords:trace theorem; anisotropic Sobolev spaces; initial boundary value problem; symmetric hyperbolic systems; characteristic boundary of constant multiplicity; characteristic mixed problem × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Guès, O.: Problème mixte hyperbolique quasilineáire charactèristique, Comm. Partial Differential Equations. 15 , 595-645 (1990). · Zbl 0712.35061 · doi:10.1080/03605309908820701 [2] Ohno, M., Shizuta, Y., and Yanagisawa, T.: The trace theorem of anisotropic Sobolev spaces. Tôhoku Math. J., 46 , 393-401 (1994). · Zbl 0810.46029 · doi:10.2748/tmj/1178225719 [3] Secchi, P.: Linear symmetric hyperbolic systems with characteristic boundary. Math. Methods Appl. Sci., 18 , 855-870 (1995). · Zbl 0837.35085 · doi:10.1002/mma.1670181103 [4] Schwartz, L.: Cours d’Analyse, Hermann, Paris (1967). [5] Shizuta, Y. and Yabuta, K.: The trace theorems in anisotropic sobolev spaces and their applications to the characteristic initial boundary value problem for symmetric hyperbolic systems. Math. Models Methods Appl. Sci., 5 , 1079-1092(1995). · Zbl 0846.35078 · doi:10.1142/S0218202595000565 [6] Shizuta, Y. and Tanaka, Y.: On a refinement of the regularity theorem for solutions to the characteristic initial boundary value problem for linear symmetric hyperbolic systems. Proc. Japan Acad., 76A , 31-34 (2000). · Zbl 0956.35080 · doi:10.3792/pjaa.76.31 [7] Yamamoto, Y.: Regularity of solutions of initial boundary value problems for symmetric hyperbolic systems with boundary characteristic of constant multiplicity. Advances in Nonlinear Partial Differential Equations and Stochastics (eds. Kawashima, S., and Yanagisawa, T.). World Scientific, Singapore, pp. 133-159 (1998). · Zbl 0917.35072 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.