References
- S. Agmon, A. Douglis and L. Nirenberg. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Communications on Pure Applied Mathematics, 12(4):623–727, 1959. https://doi.org/10.1002/cpa.3160120405. doi: 10.1002/cpa.3160120405
- M. Agranovich. Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains. Springer Monographs in Mathematics. Springer International Publishing, Berlin, 2015. https://doi.org/10.1007/978-3-319-14648-5. doi: 10.1007/978-3-319-14648-5
- R. Courant and D. Hilbert. Methods of Mathematical Physics, volume I. Wiley, New York, 1989.
- D. Daners and J.B. Kennedy. On the asymptotic behaviour of the eigenvalues of a Robin problem. Differential and Integral Equations, 23(7–8):659–669, 2010.
- P. Exner, A. Minakov and L. Parnovski. Asymptotic eigenvalue estimates for a Robin problem with a large parameter. Portugaliae Mathematica, 72(2):141–156, 2014. https://doi.org/10.4171/PM/1945. doi: 10.4171/PM/1945
- A.V. Filinovskiy. Asymptotic behavior of the first eigenvalue of the Robin problem. On the seminar on qualitative theory of differential equations at Moscow State University. Differential Equations, 47(11):1680–1696, 2011. https://doi.org/10.1134/S0012266111110152. doi: 10.1134/S0012266111110152
- A.V. Filinovskiy. Estimates of eigenvalues of a boundary value problem with a parameter. Mathematical Communications, 19(3):531–543, 2014.
- A.V. Filinovskiy. On the eigenvalues of a Robin problem with a large parameter. Mathematica Bohemica, 139(2):341–352, 2014.
- A.V. Filinovskiy. On the estimates of eigenvalues of the boundary value problem with large parameter. Tatra Mountains Mathematical Publications, 63(1):101–113, 2015. https://doi.org/10.1515/tmmp-2015-0023.
- J.L. Kazdan. Perturbation of complete orthonormal sets and eigenfunction expansions. Proceedings of the American Mathematical Society, 27(3):506–510, 1971.
- V.A. Kondratiev and E.M. Landis. Qualitative theory of second order linear partial differential equations. In Partial Differential Equations – 3, volume 32 of Itogi Nauki i Tekhniki. Sovremennye Problemy Matematiki. Fundamental’nye Napravleniya., pp. 99–215, Moscow, 1988. VINITI.
- A.A. Lacey, J. Sabina and J.R. Ockendon. Multidimensional reaction diffusion equations with nonlinear boundary conditions. SIAM Journal on Applied Mathematics, 58(5):1622–1647, 1998. https://doi.org/10.1137/S0036139996308121. doi: 10.1137/S0036139996308121
- O.A. Ladyzhenskaya. The mixed Problem for a Hyperbolic Equation. GTTI, Moscow, 1953.
- Y. Lou and M. Zhu. A singularly perturbed linear eigenvalue problem in C1 domains. Pacific Journal of Mathematics, 214(2):323–334, 2004. https://doi.org/10.2140/pjm.2004.214.323. doi: 10.2140/pjm.2004.214.323
- V.P. Mikhailov. Partial Differential Equations. Nauka, Moscow, 1983.
- S.G. Mikhlin. Numerical Realization of Variational Methods. Nauka, Moscow, 1966.
- K. Pankrashkin and N. Popoff. Mean curvature bounds and eigenvalues of Robin Laplacians. Calculus of Variations and Partial Differential Equations, 54(2):1947–1961, 2015. https://doi.org/10.1007/s00526-015-0850-1. doi: 10.1007/s00526-015-0850-1
- H.L. Smolitskiy. Some integral estimates to the derivatives of solutions of the wave equation. Doklady Akademii Nauk, 73(2):279–282, 1950.
- R. Sperb. Untere und obere Schranken für den tiefsten Eigenwert elastisch gestützten Membran. Zeitschrift fr angewandte Mathematik und Physik ZAMP, 23(2):231–244, 1972. https://doi.org/10.1007/BF01593087. doi: 10.1007/BF01593087