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Literatur
Courant, R., & D.Hilbert, Methods of Mathematical Physics, vol. II. New York-London: Interscience Publishers 1962.
Genov, A., Some uniqueness theorems for elliptic equations which are degenerate on the whole boundary. Godisnik Visš. Tehn. Učebn. Zaved. Mat.2 (1965), kn. 2, 141–146 (1967).
Genov, A., Elliptic-parabolic equations which are degenerate on the whole boundary. Godisnik Visš. Tehn. Učebn. Zaved. Mat.2 (1965), kn. 2, 147–152 (1967).
Hellwig, G., Partielle Differentialgleichungen. Stuttgart: Teubner 1960.
Hersch, J., Sur la fréquence fondamentale d'une membrane vibrante: évaluation par défaut et principe de maximum. Z. Angew. Math. Phys.11, 387–413 (1960).
Hooker, W., & M. H.Protter, Bounds for the first eigenvalue of a rhombic membrane. J. Math. Phys.39, 18–34 (1960).
Miranda, C., Partial Differential Equations of Elliptic Type. Berlin-Heidelberg-New York: Springer 1970.
Oleinik, O. A., On a problem of G. Fichera. Dokl. Akad. Nauk SSSR157, 1297–1300 (1964).
Oleinik, O. A., On the smoothness of solutions of degenerating elliptic and parabolic equations. Sov. Math. Dokl.6, 972–976 (1965).
Oleinik, O. A., On linear equations of the second order with a non-negative characteristic form. Mat. Sb. (N.S.)69 (111), 111–140 (1966).
Payne, L. E., New isoperimetric inequalities for eigenvalues and other physical quantities. Comm. Pure Appl. Math.9, 531–542 (1956).
Peetre, J., & I. A. Rus, Sur la positivité de la fonction de Green. Math. Scand.21, 80–89 (1967).
Phillips, R. S., & L.Sarason, Elliptic parabolic equations of the second order. J. Math. Mech.17, 891–917 (1967/68).
Picone, M., Teoremi di confronto fra due equazioni lineari a derivate parziali del second'ordine, di tipo ellittico-parabolico, in più variabili reali indipendenti e alcuni loro corollari. Ann. Mat. Pura Appl. (4)84, 73–82 (1970).
Picone, M., Nuova limitazione per gli autovalori di un parametro da cui dipende un'equazione lineare a derivate parziali, del second'ordine, di tipo ellittico-parabolico in quante si vogliano variabili reali indipendenti. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8)48, 152–154 (1970).
Pisters, M., A priori Abschätzungen und Regularitätsaussagen bei elliptischen Differentialgleichungen 2. Ordnung und deren Anwendung auf die Störungstheorie. Dissertation an der RWTH Aachen (1971).
Pólya, G., & G.Szegö, Isoperimetric Inequalities in Mathematical Physics. Princeton: University Press 1951.
Protter, M. H., & H. F.Weinberger, Maximum Principles in Differential Equations. Englewood Cliffs: Prentice Hall 1967.
Protter, M. H., & H. F.Weinberger, On the spectrum of general second order operators. Bull. Amer. Math. Soc.72, 251–255 (1966).
Protter, M. H., Lower bounds for the first eigenvalue of elliptic equations. Ann. of Math.71, 423–444 (1960).
Pucci, C., Maximum and minimum first eigenvalues for a class of elliptic operators. Proc. Amer. Math. Soc.17, 788–795 (1966).
Raičinov, I., A class of degenerate elliptic equations. Godišnik Visš. Tehn. Učebn. Zaved. Mat.1 (1964), kn. 1, 117–154 (1965).
Suzuki, K., The first boundary value problem and the first eigenvalue problem for the elliptic equations degenerate on the boundary. Publ. Res. Inst. Math. Sci. Ser. A3, 299–335 (1967/68).
Tersenov, S. A., On the first boundary value problem for equations of elliptic type degenerating on the boundary. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8)44, 311–316 (1968).
Watson, G. N., Theory of Bessel Functions. Cambridge: University Press 1922.
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Pisters, M. Eindeutigkeitssätze für die Dirichletsche Randwertaufgabe bei elliptisch-parabolischen Differentialgleichungen und untere Schranken für den kleinsten Eigenwert. Arch. Rational Mech. Anal. 50, 176–193 (1973). https://doi.org/10.1007/BF00703967
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DOI: https://doi.org/10.1007/BF00703967