Zobrazeno 1 - 10
of 124
pro vyhledávání: '"GARETTO, CLAUDIA"'
This paper continues the analysis of Schr\"odinger type equations with distributional coefficients initiated by the authors in [3]. Here we consider coefficients that are tempered distributions with respect to the space variable and are continuous in
Externí odkaz:
http://arxiv.org/abs/2408.02642
Autor:
Garetto, Claudia, Sabitbek, Bolys
In this paper, we study higher order hyperbolic pseudo-differential equations with variable multiplicities. We work in arbitrary space dimension and we assume that the principal part is time-dependent only. We identify sufficient conditions on the ro
Externí odkaz:
http://arxiv.org/abs/2405.04927
In this paper we investigate the well-posedness of the Cauchy problem for a Schr\"odinger operator with singular lower order terms. We allow distributional coefficients and we approach this problem via the regularising methods at the core of the theo
Externí odkaz:
http://arxiv.org/abs/2402.07826
Autor:
Garetto, Claudia, Sabitbek, Bolys
Publikováno v:
Math. Ann. (2024)
In this paper we continue the analysis of non-diagonalisable hyperbolic systems initiated in \cite{GarJRuz, GarJRuz2}. Here we assume that the system has discontinuous coefficients or more in general distributional coefficients. Well-posedness is pro
Externí odkaz:
http://arxiv.org/abs/2305.12832
This paper complements the study of the wave equation with discontinuous coefficients initiated in \cite{DGL:22} in the case of time-dependent coefficients. Here we assume that the equation coefficients are depending on space only and we formulate Le
Externí odkaz:
http://arxiv.org/abs/2208.03477
Autor:
Garetto, Claudia
This paper contributes to the wider study of hyperbolic equations with multiplicities. We focus here on some classes of higher order hyperbolic equations with space dependent coefficients in any space dimension. We prove Sobolev well-posedness of the
Externí odkaz:
http://arxiv.org/abs/2206.09377
This paper is devoted to the study of the inhomogeneous wave equation with singular (less than continuous) time dependent coefficients. Particular attention is given to the role of the lower order terms and suitable Levi conditions are formulated in
Externí odkaz:
http://arxiv.org/abs/2111.11149
Autor:
Garetto, Claudia
In this paper we study the well-posedness of the Cauchy problem for a wave equation with multiplicities and space-dependent irregular coefficients. As in \cite{GR:14} in order to give a meaningful notion of solution, we employ the notion of very weak
Externí odkaz:
http://arxiv.org/abs/2004.09657
In this paper we continue the study of non-diagonalisable hyperbolic systems with variable multiplicity started by the authors in \cite{Garetto2018}. In the case of space dependent coefficients, we prove a representation formula for solutions that al
Externí odkaz:
http://arxiv.org/abs/2001.04709
Publikováno v:
Math. Ann., 372 (2018), 1597-1629
In this paper we analyse the well-posedness of the Cauchy problem for a rather general class of hyperbolic systems with space-time dependent coefficients and with multiple characteristics of variable multiplicity. First, we establish a well-posedness
Externí odkaz:
http://arxiv.org/abs/1801.03573