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Research

Publications: Dr Claudia Garetto

Discacciati M, Garetto C, Loizou C ( 2022 ) . On the wave equation with space dependent coefficients: singularities and lower order terms .
Discacciati M, Garetto C, Loizou C ( 2022 ) . Inhomogeneous Wave Equation with T-Dependent Singular Coefficients . Journal of Differential Equations
Discacciati M, Garetto C, Loizou C ( 2021 ) . Inhomogeneous wave equation with $t$-dependent singular coefficients .
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 ( 2020 ) . Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, II: microlocal analysis .
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, Jäh C, Ruzhansky M ( 2018 ) . Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, I. Well-posedness .
Garetto C, Ruzhansky M ( 2017 ) . On C<sup>∞</sup> well-posedness of hyperbolic systems with multiplicities . Annali di Matematica Pura ed Applicata vol. 196 , ( 5 ) 1819 - 1834 .
Garetto C, Jäh C ( 2017 ) . 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, Jäh C ( 2016 ) . Well-posedness of hyperbolic systems with multiplicities and smooth coefficients .
Garetto C, Ruzhansky M ( 2015 ) . On $C^\infty$ well-posedness of hyperbolic systems with multiplicities .
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 ) . On hyperbolic systems with time dependent Hölder characteristics .
Garetto C, Ruzhansky M ( 2015 ) . Hyperbolic Second Order Equations with Non-Regular Time Dependent Coefficients . Archive for Rational Mechanics and Analysis vol. 217 , ( 1 ) 113 - 154 .
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, Oberguggenberger M ( 2015 ) . 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, Ruzhansky M ( 2014 ) . Wave equation for sums of squares on compact Lie groups .
Garetto C, Ruzhansky M ( 2013 ) . Hyperbolic second order equations with non-regular time dependent coefficients .
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, Oberguggenberger M ( 2013 ) . Generalized fourier integral operator methods for hyperbolic equations with singularities . Proceedings of the Edinburgh Mathematical Society vol. 57 , ( 2 ) 423 - 463 .
Garetto C, Ruzhansky M ( 2013 ) . On weakly hyperbolic equations with analytic principal part .
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, Ruzhansky M ( 2012 ) . Weakly hyperbolic equations with non-analytic coefficients and lower order terms .
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, Ruzhansky M ( 2011 ) . On the well-posedness of weakly hyperbolic equations with time dependent coefficients .
Garetto C, Oberguggenberger M ( 2011 ) . Generalised Fourier integral operator methods for hyperbolic equations with singularities .
Garetto C, Oberguggenberger M ( 2011 ) . Symmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficients .
Garetto C, Vernaeve H ( 2011 ) . Hilbert ℂ̃-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 ℂ̃-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 ( 2009 ) . Generalized Fourier integral operators on spaces of Colombeau type . vol. 189 ,
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, Vernaeve H ( 2007 ) . Hilbert $\widetilde{\C}$-modules: structural properties and applications to variational problems .
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, Hoermann G, Oberguggenberger M ( 2006 ) . Generalized Oscillatory Integrals and Fourier Integral Operators .
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 script G sign <inf>c</inf> (Ω), script G sign(Ω) and script G sign <inf>script S sign</inf> (ℝ <sup>n</sup>) . Monatshefte fur 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 ℂ̃-modules and duality theory . Acta Applicandae Mathematicae vol. 88 , ( 1 ) 81 - 123 .
Garetto C, Hoermann G ( 2005 ) . On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets .
Garetto C, Hoermann G ( 2004 ) . Microlocal analysis of generalized functions: pseudodifferential techniques and propagation of singularities .
Garetto C ( 2004 ) . Pseudo-differential operators in algebras of generalized functions and global hypoellipticity . Acta Applicandae Mathematicae vol. 80 , ( 2 ) 123 - 174 .