RICERCA ITALIANA     

Programmi di ricerca simili:

• 1 - ANALISI NELLO SPAZIO DELLE FASI PER EQUAZIONI A DERIVATE PARZIALI
• 2 - Equazioni e sistemi ellittici e parabolici: stime a priori, esistenza e regolarità
• 3 - Equazioni di Kolmogorov
• 4 - Equazioni alle derivate parziali e disuguaglianze funzionali: aspetti quantitativi, proprietà geometriche e qualitative, applicazioni.
• 5 - Equazioni alle derivate parziali-Analisi microlocale analitica e Gevrey
• 6 - Equazioni di Kolmogorov
• 7 - Metodi Variazionali ed Equazioni Differenziali Nonlineari
• 8 - Analisi armonica
• 9 - Dinamica dei fluidi e leggi di conservazione
• 10 - Buona positura e stime di decadimento per equazioni dispersive e sistemi iperbolici

Classificazione scientifico-disciplinare

• Area scientifico disciplinare: Scienze matematiche e informatiche
  • ANALISI MATEMATICA

Classificazione brevettuale

• PHYSICS
  • COMPUTING; CALCULATING; COUNTING (score computers for games A63; combinations of writing applicances with computing devices B43K29/08)
    • COMPUTER SYSTEMS BASED ON SPECIFIC COMPUTATIONAL MODELS [N0004]
  • CONTROLLING; REGULATING (specially adapted to a particular field of use, see the relevant place for that field, e.g. A62C37/00, B03B13/00, B23Q)
    • CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS (fluid-pressure actuators or systems acting by means of fluids in general F15B; valves per se F16K; characterised by mechanical features only G05G; sensitive elements, see the appropriate subclass, e.g. G12B, subclass of G01, H01; correcting units, see the appropriate subclass, e.g. H02K)
  • MEASURING (counting G06M); TESTING
    • GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS (detecting or locating foreign bodies for diagnostic, surgical or person-identification purposes A61B; means for indicating the location of accidentally buried, e.g. snow-buried persons A63B29/02; investigating or analysing earth materials by determining their chemical or physical properties G01N; measuring electric or magnetic variables in general, other than direction or magnitude of the earth\'s field G01R; electronic or nuclear magnetic resonance arrangements G01R33/20; radar, sonar or analogous methods in general, detecting masses or objects involving these methods G01S)

Classificazione geografica

• Regione: Toscana

Bibliografia

[Al] P.Albano, Carleman estimates for the Euler-Bernoulli plate operator, Electronic J. Diff. Eq. 53 (2000),1-13.
[AB] P.Albano, A.Bove, Stratifications and the cut locus of a class of distance functions, Israel J. Math. 20 (2006).
[ABT] P.Albano, A.Bove, D.S.Tartakoff, Analytic hypo-ellipticity in the presence of lower order terms, preprint, 2006.
[AT] P.Albano, D.Tataru, Carleman estimates and boundary observability for a coupled parabolic-hyperbolic system, Electr. J. Diff. Eq. 22 (2000),1-15.
[An] F.Antoci, On the spectrum of the Laplace-Beltrami operator for p-forms for a class of warped product metrics, Adv. Math. 188 (2004), 247-293.
[AP] F. Antoci, M. Prizzi, Attractors and global averaging of non-autonomous reaction-diffusion equations in R^n, Topol. Meth. Nonlinear Anal. 20 (2002), 229-259.
[BBB] S.Benvenuti, E.Bernardi, A.Bove, Hyperbolic systems with multiple characteristics, Bull. Sci. Math. 122 (1998), 603-634.
[BB1] E.Bernardi, A.Bove, Necessary and sufficient conditions for the well-posedness of the Cauchy problem for a class of hyperbolic equations with triple characteristics, J. Anal. Math. 54 (1990), 21-59.
[BB2] E.Bernardi, A.Bove, Propagation of Gevrey singularities for hyperbolic operators with triple characteristics, I,II, Duke Math. J. 60 (1990),187-220.
[BP] J.-F.Bony, V.Petkov, Resonances for non-trapping time-periodic perturbations, J. Phys. A 37(2004), 9439-9449.
[Bo] J.-M.Bony, Sommes de carrés de fonctions dérivables, Bull. Soc. Math. France, to appear.
[BCP] J.-M.Bony, F.Colombini, L.Pernazza, On the differentiability class of the admissible square roots of regular nonnegative functions, preprint 2005.
[BN1] A.Bove, T.Nishitani, Necessary conditions for hyperbolic systems, Bull. Sci. Math. 126 (2002), 445-479.
[BN2] A.Bove, T.Nishitani, Necessary conditions for the well posedness of the Cauchy problem for hyperbolic systems, Osaka J. Math. 39 (2002), 149-179.
[BT1] A.Bove, D.S.Tartakoff, Optimal non isotropic Gevrey exponents for sums of squares of vector fields, Comm. PDE 22 (1997), 1263-1282.
[BT2] A.Bove, D.S.Tartakoff, Analytic and Gevrey regularity for some model equations, RIMS Kokyuroku Series "Microlocal Analysis and PDE in the Complex Domain'', (2000),50-61.
[BT3] A.Bove, D.S.Tartakoff, A class of sums of squares with a given Poisson-Treves stratification, J. Geom. Anal. 13 (2003), 391-420.
[Br] M.D.Bronstein, The Cauchy problem for hyperbolic operators with characteristics of variable multiplicity, Trudy Moskov. Math. Obshch. 41 (1980), 83-99.
[Ci] M. Cicognani, The Cauchy Problem for strictly hyperbolic operators with non-absolutely continuous coefficients, Tsuk. J. Math. 27 (2003), 1-12.
[C] F.Colombini, Loss of Derivatives for t to infty in strictly hyperbolic Cauchy problems, Proceedings of the Conference "Partial Differential Equations and Applications", Ferrara, March 2005, Birkhäuser, to appear.
[CDS] F.Colombini, E.De Giorgi, S.Spagnolo, Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps, Ann. Sc. Norm. Sup. Pisa 6 (1979), 511-559.
[CJS1] F.Colombini, E.Jannelli, S.Spagnolo, Well-posedness in the Gevrey classes of the Cauchy problem for a non-strictly hyperbolic equation with coefficients depending on time, Ann. Sc. Norm. Sup. Pisa 10 (1983), 291-312.
[CJS2] F. Colombini, E.Jannelli, S.Spagnolo, Nonuniqueness in hyperbolic Cauchy problems, Ann. of Math. 126 (1987), 495-524
[CLR] F. Colombini, T. Luo, J. Rauch, Uniqueness and nonuniqueness for nonsmooth divergence free transport, E.D.P., pp. XXII 1-21, Paris Ecole Polytechnique 2003.
[CM] F.Colombini, G.Métivier, The Cauchy problem for wave equations with non Lipschitz coefficients, preprint 2006.
[CPT] F.Colombini, L.Pernazza, F.Treves, A necessary condition for the local solvability of certain operators not of principal type, Proc. Conference "Hyperbolic Problems and Related Topics - Cortona, 2002", Intern. Press, Somerville, 2003, 111-120.
[D] D.Del Santo, A remark on non-uniqueness in the Cauchy problem for elliptic operators having non-Lipschitz coefficents, Proc. Conference "Hyperbolic Differential Operators and Related Topics - Paris 2000", Marcel Dekker, New York, 2003, 317-320.
[DKR] D.Del Santo, T.Kinoshita, M.Reissig, Energy estimates for strictly hyperbolic equations with low regularity in coefficients, preprint 2005.
[DP] D.Del Santo, M.Prizzi, Backward uniqueness for parabolic operators whose coefficients are non-Lipschitz-continuous in time, J. Math. Pure Appl. 84 (2005), 176-196.
[DL] R.J. Di Perna, P.-L.Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989), 511-547.
[GT] A.Gilioli, F.Treves, An example in the solvabilty theory of linear PDE's, Amer. J. Math. 96 (1974), 367-385.
[HR] F.Hirosawa, M.Reissig, Well-posedness in Sobolev spaces for second order strictly hyperbolic equations with nondifferentiable oscillating coefficients, Ann. Global Anal. Geom. 25 (2004), 99-119.
[H] L.Hörmander, The Analysis of Linear Partial Differential Operators, Vol. I-IV, Springer-Verlag, Berlin, 1983-1985.
[I] V.Ya.Ivrii, Linear hyperbolic equations, in "Encyclopaedia of Mathematical Sciences" vol.33, Springer-Verlag, Berlin, 1993.
[IP] V.Ya.Ivrii, V.M.Petkov, Necessary conditions for the correctness of the Cauchy problem for non-strictly hyperbolic equations, Uspehi Mat. Nauk 29 (1974), 3-70.
[K] Y.Kannai, An unsolvable hypoelliptic differential operator, Israel J. Math. 9 (1971), 306-315.
[KT] H.Koch, D. Tataru, Sharp counterexamples in unique continuation for second order elliptic equations, J. Reine Angew. Math. 542 (2002), 133-146.
[LP] P.D.Lax, R.S.Phillips, Scattering Theory, Academic Press, New York, 1989.
[LOT1] O.Liess, Y.Okada, N.Tose, Hartogs phenomena for microfunctions with holomorphic parameters, Publ. Res. Inst. Math. Sci. 37 (2001), 221-238.
[LOT2] O.Liess, Y.Okada, N.Tose, Second hyperfunctions, regular sequences and Fourier inverse transforms, Bull. Soc. Roy. Sci. Liège 70 (2001), 307-345.
[Mu1] M.K.V.Murthy, Stable critical points for the Ginzburg Landau functional on some plane domains. Variational analysis and applications, 745-764, Nonconvex Optim. Appl. 79, Springer, New York, 2005.
[Mu2] M.K.V.Murthy, Regularity for a class of sub-elliptic equations, International Conference on Recent Advances in P.D.E., Journal of Nonlinear and Convex Analysis, 7 (2006).
[NT1] L.Nirenberg, F.Treves, On local solvability of linear partial differential equations. Necessary conditions, Comm. Pure Appl. Math. 23 (1970), 1-38.
[NT2] L.Nirenberg, F.Treves, On local solvability of linear partial differential equations. Sufficient conditions, Comm. Pure Appl. Math. 23 (1970), 459-509.
[PP1] C.Parenti, A.Parmeggiani, Lower bounds for systems with double characteristics, J. Anal. Math. 86 (2002), 49-91.
[PP2] C.Parenti, A.Parmeggiani, A Lyapunov lemma for elliptic systems, Ann. Global Anal. Geom. 25 (2004), 27-41.
[PR] G.Popov, T.Rangelov, Exponential growth of the local energy for moving obstacles. Osaka J. Math. 26 (1989), 881-895.
[Pr1] M.Prizzi, On admissibility for parabolic equations in R^n, Fund. Math. 176 (2003), 261-275.
[Pr2] M.Prizzi, Averaging, Conley Index continuation and recurrent dynamics in almost-periodic parabolic equations, J. Differential Equations 210 (2005), 429-451.
[TV] G. Taglialatela, J. Vaillant, Conditions invariantes d'hyperbolicité des systèmes et réduction des systèmes, Bull. Sc. Math. 120 (1996), 19-97.
[Tt] D.Tataru, On the Fefferman-Phong inequality and related problems. Comm. PDE 27 (2002), 2101-2138.
[Te] F.Treves, Symplectic geometry and analytic hypoellipticity, Proc. Symposia Pure Math. 65 (1999), 201-219.
[Z] E.Zuazua, Controllability and observability of partial differential equations: some results and open problems, in "Handbook of Differential Equations: Evolutionary Differential Equations" vol. 3, Elsevier, to appear.

Parole Chiave

ANALISI MICROLOCALE, STIME DI CARLEMAN, UNICITA' E NON UNICITA', OPERATORI A COEFFICIENTI POCO REGOLARI, PROBLEMA DI CAUCHY PER OPERATORI IPERBOLICI, IPOELLITTICITA' ANALITICA E GEVREY, LOCALE RISOLUBILITA', STIME DAL BASSO PSEUDODIFFERENZIALI, SECONDE IPERFUNZIONI