Abstract
This chapter is devoted to application of the combined estimates method to the study of dynamic problems that are neither hyperbolic nor parabolic. The Dirichlet problem for the Schroedinger equation is considered in a plane domain with corners. In such a domain, we also discuss a problem for the Germain-Lagrange dynamic plate equation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Kokotov A.Yu. and Plamenevskii B.A., On the Cauchy-Dirichlet problem for hyperbolic systems in a wedge, St.Petersburg Math. J., 11 (2000), no. 3, 497–534.
V. A. Kozlov, V. G. Maz’ya, “Singularities of solutions of the first boundary value problem for the heat equation in domains with conical points. II”, Izv. Vyssh. Uchebn. Zaved. Mat., 1987, no. 3, 37–44; Soviet Math. (Iz. VUZ), 31:3 (1987), 61–74.
Kozlov V.A., Maz’ya V.G., Rossmann J., Spectral problems associated with corner singularities of solutions to elliptic equations. Amer.Math.Soc., Mathematical Surveys Monogr., vol. 85, 2001.
Nazarov, S. A., Plamenevskii, B. A., Elliptic Problems in Domains with Piecewise Smooth Boundaries, De Gruyter Exposition in Mathematics 13, Berlin-New York, 1994.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Korikov, D., Plamenevskii, B., Sarafanov, O. (2021). Schroedinger and Germain-Lagrange Equations in a Domain with Corners. In: Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains. Operator Theory: Advances and Applications(), vol 284. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-65372-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-65372-9_6
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-65371-2
Online ISBN: 978-3-030-65372-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)