Lasiecka, Triggiani: Sharp regularity theory for second order hyperbolic equations of Neumann type

Lasiecka, Irena and Triggiani, Roberto:
Sharp regularity theory for second order hyperbolic equations of Neumann type (Regolarità delle soluzioni di equazioni differenziali iperboliche del secondo ordine con dati al contorno di tipo Newmann)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 83 (1989), fasc. n.1, p. 109-113, (English)
pdf (560 Kb), djvu (483 Kb). | MR 1142447 | Zbl 0767.35043

Sunto

Si danno risultati di regolarità delle soluzioni del problema misto per equazioni a derivate parziali del secondo ordine di tipo iperbolico, con dato non omogeneo sulla frontiera di tipo Neumann.

Referenze Bibliografiche

[1] LIONS J.L., private communication, May 1984.

[2] LIONS J.L. and MAGENES E., 1972. Nonhomogeneous boundary value problems and applications. Vols. I, II, Springer-Verlag, Berlin-Heidelberg-New York. | Zbl 0227.35001

[3] LASIECKA I. and TRIGGIANI R., 1981. A cosine operator approach to modelling $L_{2},T; L_{2}(\Gamma)$-boundary input hyperbolic equations. Applied Mathem. & Optimiz., 7: 35-93. | fulltext (doi) | MR 600559 | Zbl 0473.35022

[4] LASIECKA I. and TRIGGIANI R., 1983. Regularity of hyperbolic equations under $L_{2},T; L_{2}(\Gamma)$-boundary terms. Applied Mathem. & Optimiz., 10: 275-286. | fulltext (doi) | MR 722491 | Zbl 0526.35049

[5] LASIECKA I. and TRIGGIANI R., 1989. Trace regularity of the solutions of the wave equations with homogeneous Neumann boundary conditions. J.M.A.A., 141: 49-71. | fulltext (doi) | MR 1004583 | Zbl 0686.35029

[6] LASIECKA I., LIONS J.L. and TRIGGIANI R., 1986. Nonhomogeneous boundary value problems for second order hyperbolic operators. J. de Mathématiques Pures et Appliquées, 65: 149-192. | MR 867669 | Zbl 0631.35051

[7] MIYATAKE S., 1973. Mixed problems for hyperbolic equations of second order. J. Math. Kyoto University, 13: 435-487. | fulltext (doi) | MR 333467 | Zbl 0281.35052

[8] SAKAMOTO R., 1970. Mixed problems for hyperbolic equations. I, II. J. Math. Kyoto University, 10-2: 343-373 and 10-3: 403-417. | fulltext (doi) | MR 283400 | Zbl 0203.10001

[9] SYMES W.W., 1983. A trace theorem for solutions of the wave equation and the remote determination of acoustic sources. Mathematical Methods in the Applied Sciences, 5: 131-152. | fulltext (doi) | MR 703950 | Zbl 0528.35085

[10] TRIGGIANI R., 1978. A cosine operator approach to modeling $L_{2},T; L_{2}(\Gamma)$-boundary input problems for hyperbolic systems. In «Proceedings 8th IFIP Conference on Optimization Techniques, University of Würzburg, West Germany 1977», Springer-Verlag, Lecture Notes CIS M6: 380-390.

[11] LASIECKA I. and TRIGGIANI R., 1988. A lifting theorem for the time regularity of solutions to abstract equations with unbounded operators and applications to hyperbolic equations. Proceedings Americ. Mathem. Soc., 104: 745-755. | fulltext (doi) | MR 964851 | Zbl 0699.47034

[12] LASIECKA I. and TRIGGIANI R., Sharp regularity theory for second order hyperbolic equations of Neumann type. Part I: $L_{2}$ non-homodeneous data. Annali di Matematica Pura e Applicata, to appear. | Zbl 0742.35015

[13] LASIECKA I. and TRIGGIANI R., 1989. Regularity theory of hyperbolic equations with non-homogeneous Neumann boundary conditions. Part II: General boundary data. J. Differ. Eqts., to appear. | fulltext (doi) | MR 1133544 | Zbl 0776.35030

bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Sunto

Referenze Bibliografiche