17 citations · 38 across the 17 of their papers we have counts for
17 papers
Degenerate 3-evolution equations in Gevrey classes
Alexandre Arias Junior, Alessia Ascanelli
We consider the Cauchy problem for third-order evolution differential operators with variable coefficients, depending on time and space , where the lea…
Smoothing effect for higher order dispersive equations and applications to nonlinear initial value problems
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello
In this paper we deal with the initial value problem related to a family of dispersive inhomogeneous evolution equations Pu=f with variable coefficients belonging to the class of p…
Schwartz very weak solutions for Schrödinger type equations with distributional coefficients
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello +1
This paper continues the analysis of Schrödinger type equations with distributional coefficients initiated by the authors in [3]. Here we consider coefficients that are tempered di…
The Cauchy problem for -evolution equations with variable coefficients in Gevrey classes
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello +1
We study the Cauchy problem for a class of linear evolution equations of arbitrary order with coefficients depending both on time and space variables. Under suitable decay assumpti…
Schrödinger type equations with singular coefficients and lower order terms
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello +1
In this paper we investigate the well-posedness of the Cauchy problem for a Schrödinger operator with singular lower order terms. We allow distributional coefficients and we approa…
On the Cauchy problem for -evolution equations with variable coefficients: a necessary condition for Gevrey well-posedness
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello
In this paper we consider a class of -evolution equations of arbitrary order with variable coefficients depending on time and space variables . We prove necessary conditi…
KdV-type equations in projective Gevrey classes
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello
We prove well-posedness of the Cauchy problem for a class of third order quasilinear evolution equations with variable coefficients in projective Gevrey spaces. The class considere…
Solution theory to semilinear stochastic equations of Schrödinger type on curved spaces I -- Operators with uniformly bounded coefficients
Alessia Ascanelli, Sandro Coriasco, André Süß
We study the Cauchy problem for Schrödinger type stochastic partial differential equations with uniformly bounded coefficients on a curved space. We give conditions on the coeffici…
Gevrey well posedness for -evolution equations with variable coefficients
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello
We study the Cauchy problem for a class of third order linear anisotropic evolution equations with complex valued lower order terms depending both on time and space variables. Unde…
Solution theory to semilinear parabolic stochastic partial differential equations with polynomially bounded coefficients
Alessia Ascanelli, Sandro Coriasco, André Suß
We study function-valued solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equat…
The Cauchy problem for -evolution equations with data in Gelfand-Shilov spaces
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello
We consider the Cauchy problem for a -evolution operator with -depending coefficients and complex valued lower order terms. We assume the initial data to be Gevrey re…
Deterministic and Stochastic Cauchy problems for a class of weakly hyperbolic operators on R^n
Ahmed Abdeljawad, Alessia Ascanelli, Sandro Coriasco
We study a class of hyperbolic Cauchy problems, associated with linear operators and systems with polynomially bounded coefficients, variable multiplicities and involutive characte…
Solution theory to Semilinear Hyperbolic Stochastic Partial Differential Equations with polynomially bounded coefficients
Alessia Ascanelli, Sandro Coriasco, André Süß
We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under…
Semilinear p-evolution equations in Sobolev spaces
Alessia Ascanelli, Chiara Boiti
We prove local in time well-posedness in Sobolev spaces of the Cauchy problem for semi-linear p-evolution equations of the first order with real principal part, but complex valued…
A necessary condition for well-posedness of p-evolution equations
A. Ascanelli, C. Boiti, L. Zanghirati
We consider p-evolution equations, for , with complex valued coefficients. We prove that a necessary condition for well-posedness of the associated Cauchy proble…
Random-field Solutions to Linear Hyperbolic Stochastic Partial Differential Equations with Variable Coefficients
Alessia Ascanelli, André Süß
In this article we show the existence of a random-field solution to linear stochastic partial differential equations whose partial differential operator is hyperbolic and has varia…
Weighted energy estimates for -evolution equations
Alessia Ascanelli, Marco Cappiello
We prove energy estimates for linear -evolution equations in weighted Sobolev spaces under suitable assumptions on the behavior at infinity of the coefficients with respect to t…