Skip to main content
Research
  1. Queen Mary University of London
  2. Research
  3. Publications

Publications: Dr Claudia Garetto

Back to Search
Discacciati M, Garetto C, Loizou C ( 2023 ) . On the Wave Equation with Space Dependent Coefficients: Singularities and Lower Order Terms . Acta Applicandae Mathematicae vol. 187 , ( 1 )
Discacciati M, Garetto C, Loizou C ( 2022 ) . Inhomogeneous Wave Equation with T-Dependent Singular Coefficients . Journal of Differential Equations
Garetto C ( 2021 ) . On the wave equation with multiplicities and space-dependent irregular coefficients . Transactions of the American Mathematical Society vol. 374 , ( 5 ) 3131 - 3176 .
Garetto C, Jäh C, Ruzhansky M ( 2020 ) . Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, II: microlocal analysis . Journal of Differential Equations
Garetto C, Jäh C, Ruzhansky M ( 2018 ) . Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, I: well-posedness . Mathematische Annalen vol. 372 , ( 3-4 ) 1597 - 1629 .
Garetto C, Ruzhansky M ( 2017 ) . On C∞ well-posedness of hyperbolic systems with multiplicities . Annali di Matematica Pura ed Applicata (1923 -) vol. 196 , ( 5 ) 1819 - 1834 .
Garetto C, Jäh C ( 2016 ) . Well-posedness of hyperbolic systems with multiplicities and smooth coefficients . Mathematische Annalen vol. 369 , ( 1-2 ) 441 - 485 .
Garetto C, Ruzhansky M ( 2016 ) . On hyperbolic systems with time-dependent Hölder characteristics . Annali di Matematica Pura ed Applicata vol. 196 , ( 1 ) 155 - 164 .
Garetto C ( 2015 ) . On hyperbolic equations and systems with non-regular time dependent coefficients . Journal of Differential Equations vol. 259 , ( 11 ) 5846 - 5874 .
Garetto C, Ruzhansky M ( 2015 ) . Wave equation for sums of squares on compact Lie groups . Journal of Differential Equations vol. 258 , ( 12 ) 4324 - 4347 .
Garetto C, Ruzhansky M ( 2014 ) . Hyperbolic Second Order Equations with Non-Regular Time Dependent Coefficients . Archive for Rational Mechanics and Analysis vol. 217 , ( 1 ) 113 - 154 .
Garetto C, Oberguggenberger M ( 2014 ) . Symmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficients . Mathematische Nachrichten vol. 288 , ( 2-3 ) 185 - 205 .
Garetto C, Ruzhansky M ( 2014 ) . A note on weakly hyperbolic equations with analytic principal part . Journal of Mathematical Analysis and Applications vol. 412 , ( 1 ) 1 - 14 .
Garetto C, Oberguggenberger M ( 2013 ) . Generalized Fourier Integral Operator Methods for Hyperbolic Equations with Singularities . Proceedings of the Edinburgh Mathematical Society vol. 57 , ( 2 ) 426 - 463 .
Garetto C, Ruzhansky M ( 2013 ) . Weakly hyperbolic equations with non-analytic coefficients and lower order terms . Mathematische Annalen vol. 357 , ( 2 ) 401 - 440 .
Garetto C, Ruzhansky M ( 2012 ) . On the well-posedness of weakly hyperbolic equations with time-dependent coefficients . Journal of Differential Equations vol. 253 , ( 5 ) 1317 - 1340 .
Garetto C ( 2011 ) . Lp and Sobolev boundedness of pseudodifferential operators with non-regular symbol: A regularisation approach . Journal of Mathematical Analysis and Applications vol. 381 , ( 1 ) 328 - 343 .
Garetto C, Vernaeve H ( 2010 ) . Hilbert C ~ \widetilde {\mathbb {C}} -modules: Structural properties and applications to variational problems . Transactions of the American Mathematical Society vol. 363 , ( 4 ) 2047 - 2090 .
Garetto C ( 2009 ) . Sufficient conditions of local solvability for partial differential operators on spaces of colombeau type . Electronic Journal of Differential Equations vol. 2009 , 1 - 43 .
Garetto C ( 2009 ) . Closed graph and open mapping theorems for topological $ \tilde \lc $‐modules and applications . Mathematische Nachrichten vol. 282 , ( 8 ) 1159 - 1188 .
Garetto C, Hörmann G, Oberguggenberger M ( 2009 ) . Generalized oscillatory integrals and Fourier integral operators . Proceedings of the Edinburgh Mathematical Society vol. 52 , ( 2 ) 351 - 386 .
Garetto C ( 2008 ) . Fundamental Solutions in the Colombeau Framework: Applications to Solvability and Regularity Theory . Acta Applicandae Mathematicae vol. 102 , ( 2-3 ) 281 - 318 .
Garetto C ( 2008 ) . Generalized Fourier Integral Operators on Spaces of Colombeau Type . New Developments in Pseudo-Differential Operators , Springer Nature
Garetto C ( 2006 ) . Microlocal analysis in the dual of a Colombeau algebra: Generalized wave front sets and noncharacteristic regularity . New York Journal of Mathematics vol. 12 , 275 - 318 .
Garetto C, Hormann G ( 2006 ) . On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets . Bulletin Classe des sciences mathematiques et natturalles vol. 133 , ( 31 ) 115 - 136 .
Garetto C ( 2005 ) . Topological Structures in Colombeau Algebras: Investigation of the Duals of , and . Monatshefte für Mathematik vol. 146 , ( 3 ) 203 - 226 .
Garetto C, Gramchev T, Oberguggenberger M ( 2005 ) . Pseudodifferential operators with generalized symbols and regularity theory . Electronic Journal of Differential Equations vol. 2005 ,
Garetto C, Hörmann G ( 2005 ) . MICROLOCAL ANALYSIS OF GENERALIZED FUNCTIONS: PSEUDODIFFERENTIAL TECHNIQUES AND PROPAGATION OF SINGULARITIES . Proceedings of the Edinburgh Mathematical Society vol. 48 , ( 3 ) 603 - 629 .
Garetto C ( 2005 ) . Topological Structures in Colombeau Algebras: Topological -modules and Duality Theory . Acta Applicandae Mathematicae vol. 88 , ( 1 ) 81 - 123 .
Garetto C ( 2004 ) . Pseudo-Differential Operators in Algebras of Generalized Functions and Global Hypoellipticity . Acta Applicandae Mathematicae vol. 80 , ( 2 ) 123 - 174 .
Back to Search