arXiv subjects
Publications and source records attributed to Isolda Cardoso.
We find integrability conditions on the initial data $f$ for the existence of solutions of the Heat problem on the Heisenberg group. From this result we characterize the weighted Lebesgue spaces for which the solutions exists a.e. when the time goes to zero. Finally we also obtain boundedness of the local maximal function associated to the heat kernel with weights.
The traffic assignment problem (TAP) aims to predict how traffic flows distribute themselves across a road network, traditionally requiring computationally expensive iterative simulations to reach a user equilibrium (UE) where no driver can unilaterally reduce their travel time. Recent developments in machine learning (ML), particularly Graph Neural Networks (GNNs) and hybrid approaches, aim to solve this faster while maintaining accuracy
A real Lie algebra is said to be characteristically solvable if its derivation algebra is solvable. We explicitly determine the moduli space of left-invariant metrics, up to isometric automorphism, for $6$-dimensional nilmanifolds whose associated Lie algebra is characteristically solvable of triangular type. We also compute the corresponding full isometry groups. For each left-invariant metric on these nilmanifolds we compute the index and distribution of symmetry. In particular, we find the first known examples of Lie groups which do not admit a left-invariant metric with positive index of symmetry. As an application we study the index of symmetry of nilsoliton metrics. We prove that nilsoliton metrics detect the existence of left-invariant metrics with positive index of symmetry.
We consider a family of initial boundary value problems governed by a fractional diffusion equation with Caputo derivative in time, where the parameter is the Newton heat transfer coefficient linked to the Robin condition on the boundary. For each problem we prove existence and uniqueness of solution by a Fourier approach. This will enable us to also prove the convergence of the family of solutions to the solution of the limit problem, which is obtained by replacing the Robin boundary condition with a Dirichlet boundary condition.
Let Omega be a non-empty open proper and connected subset of R^n. Consider p elliptic Schrödinger type operator L_{E}u=A_{E}u+V in Omega, and the linear parabolic operator L_{P}u=A_{P}u+Vu in Omega x (0,T), where the coefficients of A_{E} and A_{P} are in VMO and the potential V satisfies a reverse-Hölder condition. The aim of this paper is to obtain a priori estimates for the operators L_{E} and L_{P} in weighted Sobolev spaces involving the distance to the boundary and weights in a local-A class.
We find optimal integrability conditions on the initial data $f$ for the existence of solutions $e^{-tΔ_λ}f(x)$ and $e^{-t\sqrt{Δ_λ}}f(x)$ of the heat and Poisson initial data problems for the Bessel operator $Δ_λ$ in $\mathbb{R}^{+}$. We also characterize the most general class of weights $v$ for which the solutions converge a.e. to $f$ for every $f\in L^{p}(v)$, with $1\le p<\infty$. Finally, we show that for such weights and $1<p<\infty$ the local maximal operators are bounded from $L^{p}(v)$ to $L^{p}(u)$, for some weight $u$.
Let $p,q,n$ be natural numbers such that $p+q=n$. Let $\FF$ be either $\CC$, the complex numbers field, or $\HH$, the quaternionic division algebra. We consider the Heisenberg group $N(p,q,\FF)$ defined as $N(p,q,\FF)=\FF^{n}\times \mathfrak{Im}\FF$, with group law given by $$(v,ζ)(v',ζ')=(v+v', ζ+ζ'-{1/2} \mathfrak{Im} B(v,v')),$$ where $B(v,w)=\sum_{j=1}^{p} v_{j}\bar{w_{j}} - \sum_{j=p+1}^{n} v_{j}\bar{w_{j}}$. Let $U(p,q,\FF)$ be the group of $n\times n$ matrices with coefficients in $\FF$ that leave invariant the form $B$. In this work we compute explicit fundamental solutions of some second order differential operators on $N(p,q,\FF)$ which are canonically associated to the action of $U(p,q,\FF)$.