A characterization of elliptic operators
We give a characterization of constant coefficients elliptic operators in terms of estimates of their iterations on smooth functions.
A condition on the potential for the existence of doubly periodic solutions of a semi-linear fourth-order partial differential equation.
A maximum principle for biharmonic functions in Lipschitz and C1 domains.
A polyharmonic analogue of a Lelong theorem and polyhedric harmonicity cells.
A remark on the solvability of the Dirichlet problem in Sobolev spaces with power-type weights
A simple proof of the characterization of functions of low Aviles Giga energy on a ball via regularity
The Aviles Giga functional is a well known second order functional that forms a model for blistering and in a certain regime liquid crystals, a related functional models thin magnetized films. Given Lipschitz domain Ω ⊂ ℝ2the functional is I ϵ ( u ) = 1 2 ∫ Ω ϵ -1 1 − Du 2 2 + ϵ D 2 u 2 d z whereubelongs to the subset of functions in W02,2(Ω) whose gradient (in the sense of trace) satisfiesDu(x)·ηx = 1 where ηx is the inward pointing unit normal to ∂Ω at x. In [Ann. Sc. Norm. Super. Pisa Cl....
A simple proof of the characterization of functions of low Aviles Giga energy on a ball via regularity
The Aviles Giga functional is a well known second order functional that forms a model for blistering and in a certain regime liquid crystals, a related functional models thin magnetized films. Given Lipschitz domain Ω ⊂ ℝ2 the functional is where u belongs to the subset of functions in whose gradient (in the sense of trace) satisfies Du(x)·ηx = 1 where ηx is the inward pointing unit normal ...
A supersolution-subsolution method for nonlinear biharmonic equations in
A uniqueness theorem for higher order elliptic partial differential equations.
Allgemeine Darstellungssätze bei einer Klasse partieller Differentialgleichungen gerader Ordnung.
Analyticité microlocale et itères d'opérateurs
Bifurcation theorems of Rabinowitz type for certain differential operators of the fourth order
This paper was inspired by the works of P. H. Rabinowitz. We study nonlinear eigenvalue problems for some fourth order elliptic partial differential equations with nonlinear perturbation of Rabinowitz type. We show the existence of an unbounded continuum of nontrivial positive solutions bifurcating from (μ₁,0), where μ₁ is the first eigenvalue of the linearization about 0 of the considered problem. We also prove the related theorem for bifurcation from infinity. The results obtained are similar...
Characterization of some interpolation spaces (I)
Si calcolano alcuni spazi di interpolazione fra spazi di funzioni hölderiane.
Characterization of some interpolation spaces (II)
Si caratterizzano alcuni spazi di interpolazione tra spazi di funzioni continue e domini di operatori ellittici del 2° ordine.
Das Ausstrahlungsproblem für elliptische Differentialgleichungen in Gebieten mit unbeschränkten Rand.
Diagonalisation d'opérateurs non-autoadjoints et séparation des variables
Eliptické parciální diferenciální rovnice s degenerovanými koeficienty
Elliptische Differentialgleichungen mit variablen Koeffizienten in Gebieten mit unbeschränktem Rand.
Estimation du reste dans la théorie spectrale d'une classe de problèmes d'opérateur elliptiques dégénérés