American Institute of Mathematical Sciences

Advanced
July  2006, 6(4): 751-760. doi: 10.3934/dcdsb.2006.6.751

Maximal dissipativity of a class of elliptic degenerate operators in weighted $L^2$ spaces

Giuseppe Da Prato 1, and  Alessandra Lunardi 2,

1. 

Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126, Pisa, Italy
2. 

Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze 53, 43100 Parma, Italy

Received  March 2005 Revised  September 2005 Published  April 2006

We consider a degenerate elliptic Kolmogorov--type operator arising from second order stochastic differential equations in $\mathbb R^{n}$ perturbed by noise. We study a realization of such an operator in $L^2$ spaces with respect to an explicit invariant measure, and we prove that it is $m$-dissipative.
Keywords: Kolmogorov operators, Second order stochastic equations, invariant measures., degenerate elliptic operators.
Mathematics Subject Classification: 35J70, 60H10, 37L4.
Citation: Giuseppe Da Prato, Alessandra Lunardi. Maximal dissipativity of a class of elliptic degenerate operators in weighted $L^2$ spaces. Discrete & Continuous Dynamical Systems - B, 2006, 6 (4) : 751-760. doi: 10.3934/dcdsb.2006.6.751
[1]

François Hamel, Emmanuel Russ, Nikolai Nadirashvili. Comparisons of eigenvalues of second order elliptic operators. Conference Publications, 2007, 2007 (Special) : 477-486. doi: 10.3934/proc.2007.2007.477
[2]

Giuseppe Di Fazio, Maria Stella Fanciullo, Pietro Zamboni. Harnack inequality for degenerate elliptic equations and sum operators. Communications on Pure & Applied Analysis, 2015, 14 (6) : 2363-2376. doi: 10.3934/cpaa.2015.14.2363
[3]

Annamaria Canino, Elisa De Giorgio, Berardino Sciunzi. Second order regularity for degenerate nonlinear elliptic equations. Discrete & Continuous Dynamical Systems - A, 2018, 38 (8) : 4231-4242. doi: 10.3934/dcds.2018184
[4]

Angelo Favini, Gisèle Ruiz Goldstein, Jerome A. Goldstein, Silvia Romanelli. Selfadjointness of degenerate elliptic operators on higher order Sobolev spaces. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 581-593. doi: 10.3934/dcdss.2011.4.581
[5]

M. Euler, N. Euler, M. C. Nucci. On nonlocal symmetries generated by recursion operators: Second-order evolution equations. Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4239-4247. doi: 10.3934/dcds.2017181
[6]

Simona Fornaro, Giorgio Metafune, Diego Pallara, Roland Schnaubelt. Second order elliptic operators in $L^2$ with first order degeneration at the boundary and outward pointing drift. Communications on Pure & Applied Analysis, 2015, 14 (2) : 407-419. doi: 10.3934/cpaa.2015.14.407
[7]

Fausto Ferrari. Mean value properties of fractional second order operators. Communications on Pure & Applied Analysis, 2015, 14 (1) : 83-106. doi: 10.3934/cpaa.2015.14.83
[8]

Petr Hasil, Petr Zemánek. Critical second order operators on time scales. Conference Publications, 2011, 2011 (Special) : 653-659. doi: 10.3934/proc.2011.2011.653
[9]

Genni Fragnelli, Gisèle Ruiz Goldstein, Jerome Goldstein, Rosa Maria Mininni, Silvia Romanelli. Generalized Wentzell boundary conditions for second order operators with interior degeneracy. Discrete & Continuous Dynamical Systems - S, 2016, 9 (3) : 697-715. doi: 10.3934/dcdss.2016023
[10]

Andrea Bonfiglioli, Ermanno Lanconelli. Lie groups related to Hörmander operators and Kolmogorov-Fokker-Planck equations. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1587-1614. doi: 10.3934/cpaa.2012.11.1587
[11]

Liang Zhang, X. H. Tang, Yi Chen. Infinitely many solutions for a class of perturbed elliptic equations with nonlocal operators. Communications on Pure & Applied Analysis, 2017, 16 (3) : 823-842. doi: 10.3934/cpaa.2017039
[12]

Victor Isakov, Nanhee Kim. Weak Carleman estimates with two large parameters for second order operators and applications to elasticity with residual stress. Discrete & Continuous Dynamical Systems - A, 2010, 27 (2) : 799-825. doi: 10.3934/dcds.2010.27.799
[13]

Jun Cao, Der-Chen Chang, Dachun Yang, Sibei Yang. Boundedness of second order Riesz transforms associated to Schrödinger operators on Musielak-Orlicz-Hardy spaces. Communications on Pure & Applied Analysis, 2014, 13 (4) : 1435-1463. doi: 10.3934/cpaa.2014.13.1435
[14]

Alessia E. Kogoj, Ermanno Lanconelli, Giulio Tralli. Wiener-Landis criterion for Kolmogorov-type operators. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2467-2485. doi: 10.3934/dcds.2018102
[15]

Nils Svanstedt. Multiscale stochastic homogenization of monotone operators. Networks & Heterogeneous Media, 2007, 2 (1) : 181-192. doi: 10.3934/nhm.2007.2.181
[16]

Liu Yang, Xiaojiao Tong, Yao Xiong, Feifei Shen. A smoothing SAA algorithm for a portfolio choice model based on second-order stochastic dominance measures. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-15. doi: 10.3934/jimo.2018198
[17]

Siegfried Carl, Christoph Tietz. Quasilinear elliptic equations with measures and multi-valued lower order terms. Discrete & Continuous Dynamical Systems - S, 2018, 11 (2) : 193-212. doi: 10.3934/dcdss.2018012
[18]

Piermarco Cannarsa, Genni Fragnelli, Dario Rocchetti. Null controllability of degenerate parabolic operators with drift. Networks & Heterogeneous Media, 2007, 2 (4) : 695-715. doi: 10.3934/nhm.2007.2.695
[19]

Claudia Anedda, Giovanni Porru. Second order estimates for boundary blow-up solutions of elliptic equations. Conference Publications, 2007, 2007 (Special) : 54-63. doi: 10.3934/proc.2007.2007.54
[20]

Sylvain De Moor, Luis Miguel Rodrigues, Julien Vovelle. Invariant measures for a stochastic Fokker-Planck equation. Kinetic & Related Models, 2018, 11 (2) : 357-395. doi: 10.3934/krm.2018017

2018 Impact Factor: 1.008

Tools

Metrics

  • PDF downloads (5)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences