Some properties of positive superharmonic functions
Some remarks on largest subharmonic minorants.
Some uniqueness results for Bernoulli interior free-boundary problems in convex domains.
Su alcune questioni connesse con il problema di derivata obliqua regolare per le funzioni armoniche
— Vengono riconsiderati il problema di derivata obliqua regolare e quello misto di Dirichlet-derivata obliqua regolare per le funzioni armoniche in un dominio di e le questioni di completezza hilbertiana connesse già studiate in un precedente lavoro e viene data una nuova dimostrazione di un teorema di unicità.
Subharmonic functions and their Riesz measure.
Superharmonic extension and harmonic approximation
Let be an open set in and be a subset of . We characterize those pairs which permit the extension of superharmonic functions from to , or the approximation of functions on by harmonic functions on .
Superharmonic functions and differential equations involving measures for quasilinear elliptic operators with lower order terms.
Superharmonic functions on Lipschitz domain
Superharmonicity of nonlinear ground states.
The objective of our note is to prove that, at least for a convex domain, the ground state of the p-Laplacian operatorΔpu = div (|∇u|p-2 ∇u)is a superharmonic function, provided that 2 ≤ p ≤ ∞. The ground state of Δp is the positive solution with boundary values zero of the equationdiv(|∇u|p-2 ∇u) + λ |u|p-2 u = 0in the bounded domain Ω in the n-dimensional Euclidean space.
Sur le développement d'une fonction arbitraire en une série procédant suivant les fonctions harmoniques
Surface integrals and harmonic functions.
Temps locaux et l'intégrale d'aire de Lusin
Teoremi di confronto di tipo Harnack per funzioni armoniche in domini con frontiera hölderiana
The atomic decomposition of harmonic functions satisfying certain conditions of integrability.
The boundary-value problems for Laplace equation and domains with nonsmooth boundary
Dirichlet, Neumann and Robin problem for the Laplace equation is investigated on the open set with holes and nonsmooth boundary. The solutions are looked for in the form of a double layer potential and a single layer potential. The measure, the potential of which is a solution of the boundary-value problem, is constructed.
The Brothers Riesz theorem in and Laplace series.
The Cauchy transform of continuous linear functionals and projections on the weighted spaces of analytic functions.
The Dynamics of Inner Functions. / Claus I. Doering; Ricardo Mané.
The evolution and Poisson kernels on nilpotent meta-abelian groups
Let S be a semidirect product S = N⋊ A where N is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and A is isomorphic to , k>1. We consider a class of second order left-invariant differential operators on S of the form , where , and for each is left-invariant second order differential operator on N and , where Δ is the usual Laplacian on . Using some probabilistic techniques (e.g., skew-product formulas for diffusions on S and N respectively) we obtain an...
The General Riesz Decomposition and the Specific Order of Excessive Functions.