Une construction de fonctions plurisousharmoniques nous permet, en utilisant les techniques de Hörmander, d’obtenir un résultat de $d^{\text{'}\text{'}}$-cohomologie à croissance. Les méthodes de B. Malgrange nous fournissent alors deux applications aux systèmes différentiels à coefficients constants.

We study the Gevrey regularity down to t = 0 of solutions to the initial value problem for a semilinear heat equation ${\partial }_{t}u-\Delta u=u^M$. The approach is based on suitable iterative fixed point methods in $L^p$ based Banach spaces with anisotropic Gevrey norms with respect to the time and the space variables. We also construct explicit solutions uniformly analytic in t ≥ 0 and x ∈ ℝⁿ for some conservative nonlinear terms with symmetries.

L'autore dà una condizione necessaria e sufficiente per la risolubilità formale degli operatori differenziali a coefficienti costanti, lineari, $p\left(D\right)$, in termini di prolungamento, come distribuzioni, delle $u\in D^{\prime }\left({\mathbb{R}}^n-\left\{0\right\}\right)$, tali che $p\left(-D\right)u=0$.