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2008 | Vol. 37, no 4 | 831-878
Tytuł artykułu

Generation of analytic semi-groups in L² for a class of second order degenerate elliptic operators

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the generation of analytic semigroups in the L² topology by second order elliptic operators in divergence form, that may degenerate at the boundary of the space domain. Our results, that hold in two space dimensions, guarantee that the solutions of the corresponding evolution problems support integration by parts. So, this paper provides the basis for deriving Carleman type estimates for degenerate parabolic operators.
Wydawca

Rocznik
Strony
831-878
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
  • Dipartimento di Matematica, Universita di Roma "Tor Vergata" Via della Ricerca Scientifica 1, 00133 Roma, Italy, cannarsa@mat.uniroma2.it
Bibliografia
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  • AGMON, S. (1965) Elliptic Boundary Value Problems. Van Nostrand Company.
  • ALABAU-BOUSSOUIRA, F., CANNARSA, P. and FRAGNELLI, G. (2006) Carleman estimates for degenerate parabolic operators with applications to null controllability. J. Evol Eqs 6, 161-204.
  • BAIOCCHI, C. and CAPELO, A. (1983) Variational and Quasivariational Inequalities, Applications to Free Boundary Problems. Wiley, Chichester.
  • BELLMAN, R.E. (1960) Introduction to Matrix Analysis. McGraw-Hill.
  • BENSOUSSAN, A., DA PRATO, G., DELFOUR, M.C. and MITTER, S.K. (1993) Representation and Control of Infinite Dimensional Systems. Systems and Control: Foundations and applications. Birkhäuser.
  • CANNARSA, P., FRAGNELLI, G. and ROCCHETTI, D. (2007) Null Controllability of degenerate parabolic operators with drift. Networks and Heterogeneous Media 2 (4).
  • CANNARSA, P., MARTINEZ, P. and VANCOSTENOBLE, J. (2004) Persistent regional controllability for a class of degenerate parabolic equations. Commun. Pure Appl. Anal. 3, 607-635.
  • CANNARSA, P. and SINESTRARI, C. (2004) Semiconcave Functions, Hamilton-Jacobi Equations and Optimal Control. Birkhäuser, Boston.
  • CAZENAVE, T. and HARAUX, A. (1998) An Introduction to Semilinear Evolution Equations. Oxford Lecture Series in Mathematics and its Applications 13, Oxford University Press.
  • DAVIES, E.B. (1995) Spectral Theory and Differential Operators. Cambridge Univ. Press. Cambridge.
  • DELFOUR, M.C. and ZOLÉSIO, J.P. (1994) Shape analysis via oriented distance functions. J. Funct. Anal. 123(1), 129-201.
  • EGOROV, Y.V. and SHUBIN, M.A. (1994) Partial Differential Equations VI. Springer Berlin, Heidelberg, New York.
  • FICHERA, G. 1956 Sulle equazioni differenziali lineari ellittico-paraboliche del secondo ordine. Lincei - Memorie Sc. fisiche, ecc. VIII, V (I, I).
  • FREIDLIN, M. (1985) Functional Integration and Partial Differential Equations. Princeton University Press.
  • GILBARG, D. and TRUDINGER, N.S. (1983) Elliptic Partial Differential Equations of Second Order . Springer Verlag, Berlin, Heidelberg, New York, Tokyo.
  • LIONS, J.L. and MAGENES, E. (1972) Non-homogeneous Boundary Value Problems and Applications. I, Springer, Berlin.
  • MARTINEZ, P. and VANCOSTENOBLE, J. (2006) Carleman estimates for one-dimensional degenerate heat equations. J. Evol. Eqs 6, 325-362.
  • NECAS, J. (1967) Les méthodes directes en théorie des équations elliptiques. Masson.
  • OLEINIK, O.A. (1966) Alcuni risultati sulle equazioni lineari e quasi lineari ellittico-paraboliche a derivate parziali del secondo ordine. Lincei - Rend. Sc. fis. mat. e nat. XL.
  • OLEINIK, O.A. and RADKEWITCH, E.V. (1973) Second Order Equations with Non-negative Characteristic Form. American Math. Soc. and Plenum Press, New York.
  • SHOWALTER, R.E. (1977) Hilbert Space Methods for Partial Differential Equations. Pitman.
  • TEMAM, R. (1977) Navier-Stokes Equations. North Holland, Amsterdam.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0034-0005
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