We prove the unique solvability of parabolic equations with discontinuous leading coefficients in . Using this result, we establish the uniqueness of diffusion processes with time-dependent discontinuous coefficients.
Let χ be a space of homogeneous type. The aims of this paper are as follows.i) Assuming that T is a bounded linear operator on L2(χ), we give a sufficient condition on the kernel of T such that T is of weak type (1,1), hence bounded on Lp(χ) for 1 < p ≤ 2; our condition is weaker then the usual Hörmander integral condition.ii) Assuming that T is a bounded linear operator on L2(Ω) where Ω is a measurable subset of χ, we give a sufficient condition on the kernel of T so that T is of weak type...
We consider the time-harmonic eddy current problem in its electric formulation where the conductor is a polyhedral domain. By proving the convergence in energy, we justify in what sense this problem is the limit of a family of Maxwell transmission problems: Rather than a low frequency limit, this limit has to be understood in the sense of Bossavit [11]. We describe the singularities of the solutions. They are related to edge and corner singularities of certain problems for the scalar Laplace operator,...
We consider the time-harmonic eddy current problem in its electric formulation where the conductor is a polyhedral domain. By proving the convergence in energy, we justify in what sense this problem is the limit of a family of Maxwell transmission problems: Rather than a low frequency limit, this limit has to be understood in the sense of Bossavit [11]. We describe the singularities of the solutions. They are related to edge and corner singularities of certain problems for the scalar Laplace...
We investigate time harmonic Maxwell equations in heterogeneous media, where the permeability μ and the permittivity ε are piecewise constant. The associated boundary value problem can be interpreted as a transmission problem. In a very natural way the interfaces can have edges and corners. We give a detailed description of the edge and corner singularities of the electromagnetic fields.
En esta nota se analizan dos modelos matemáticos deterministas planteados en problemas ecológicos causados por la introducción de nuevas especies en ambientes insulares heterogéneos. En el primero desarrollamos un modelo epidemológico con transmisión indirecta del virus por medio del ambiente. En el segundo se introduce un modelo específico de depredador-presa que exhibe la extinción en tiempo finito de las especies. Ambos modelos involucran sistemas de ecuaciones en derivadas parciales con interesantes...
We study semilinear equations and inequalities of parabolic type with discontinuous nonlinearities, possibly subjected to convex or even nonconvex constraint conditions. To prove some existence theorems we regard the solutions as «curves of maximal relaxed slope» for a suitable functional on the given constraint.
In questo articolo consideriamo alcune semplici equazioni a derivate parziali elittiche nonlineari, per le quali il Teorema della Funzione Inversa, se applicato in modo formale, suggerisce l'esistenza di soluzioni. Nonostante ciò, proviamo che non esistono soluzioni neppure in vari sensi deboli. Un problema modello è dato da in , su , dove , , è un dominio limitato contenente . Per qualunque costante , arbitrariamente piccola, proviamo che questo problema non ammette soluzioni distribuzionali...