This note provides sharp regularity results for general, time-independent, second order, hyperbolic equations with non-homogeneous data of Neumann type.
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.
@article{RLINA_1989_8_83_1_109_0, author = {Irena Lasiecka and Roberto Triggiani}, title = {Sharp regularity theory for second order hyperbolic equations of Neumann type}, journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti}, volume = {83}, year = {1989}, pages = {109-113}, zbl = {0767.35043}, mrnumber = {1142447}, language = {en}, url = {http://dml.mathdoc.fr/item/RLINA_1989_8_83_1_109_0} }
Lasiecka, Irena; Triggiani, Roberto. Sharp regularity theory for second order hyperbolic equations of Neumann type. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 83 (1989) pp. 109-113. http://gdmltest.u-ga.fr/item/RLINA_1989_8_83_1_109_0/
[1]
, private communication, May 1984.[2] I, II, Springer-Verlag, Berlin-Heidelberg-New York. | Zbl 0227.35001
and , 1972. Nonhomogeneous boundary value problems and applications. Vols.[3] A cosine operator approach to modelling -boundary input hyperbolic equations. Applied Mathem. & Optimiz., 7: 35-93. | MR 600559 | Zbl 0473.35022
and , 1981.[4] Regularity of hyperbolic equations under -boundary terms. Applied Mathem. & Optimiz., 10: 275-286. | MR 722491 | Zbl 0526.35049
and , 1983.[5] Trace regularity of the solutions of the wave equations with homogeneous Neumann boundary conditions. J.M.A.A., 141: 49-71. | MR 1004583 | Zbl 0686.35029
and , 1989.[6] Nonhomogeneous boundary value problems for second order hyperbolic operators. J. de Mathématiques Pures et Appliquées, 65: 149-192. | MR 867669 | Zbl 0631.35051
, and , 1986.[7] Mixed problems for hyperbolic equations of second order. J. Math. Kyoto University, 13: 435-487. | MR 333467 | Zbl 0281.35052
, 1973.[8] Mixed problems for hyperbolic equations. I, II. J. Math. Kyoto University, 10-2: 343-373 and 10-3: 403-417. | MR 283400 | Zbl 0203.10001
, 1970.[9] 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. | MR 703950 | Zbl 0528.35085
, 1983.[10] A cosine operator approach to modeling -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.
, 1978.[11] 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. | MR 964851 | Zbl 0699.47034
and , 1988.[12] Sharp regularity theory for second order hyperbolic equations of Neumann type. Part I: non-homodeneous data. Annali di Matematica Pura e Applicata, to appear. | Zbl 0742.35015
and ,[13] Regularity theory of hyperbolic equations with non-homogeneous Neumann boundary conditions. Part II: General boundary data. J. Differ. Eqts., to appear. | MR 1133544 | Zbl 0776.35030
and , 1989.