Permanence of metric fractals.
Perturbation of Harmonic Spaces and Construction of Semigroups.
Pointwise and locally uniform convergence of holomorphic and harmonic functions
We shall characterize the sets of locally uniform convergence of pointwise convergent sequences. Results obtained for sequences of holomorphic functions by Hartogs and Rosenthal in 1928 will be generalized for many other sheaves of functions. In particular, our Hartogs-Rosenthal type theorem holds for the sheaf of solutions to the second order elliptic PDE's as well as it has applications to the theory of harmonic spaces.
Pointwise multipliers of Besov spaces of continuous functions.
Polynomoperatoren bei Differentialgleichungen der Form wzz + Awz + Bw = 0.
Positive Harmonic Functions on Nontangentially Accessible Domains.
Principe de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine lipschitzien
L’article étudie le compactifié de Martin d’un domaine lipschitzien relativement à un opérateur elliptique à coefficients hödériens ; on étend aux fonctions -harmoniques et aux fonctions -harmoniques adjointes sur une estimation de -Carleson pour le cas , puis on établit un “principe de Harnack à la frontière” comparant l’allure à la frontière de fonctions -harmoniques sur . Conséquences : , et normalisée en ; un théorème de type Fatou-Doob sur l’existence de limites angulaires.On...
Propriété des itérés et ellipticité
Propriétés des courbes intégrales de champs de vecteurs et estimations ponctuelles d'équation elliptiques dégénérés
Quasi-analyticité et unicité du problème de Cauchy pour les solutions d'équations aux dérivées partielles
Quasilinear degenerated equations with datum and without coercivity in perturbation terms.
Regularity of renormalized solutions to nonlinear elliptic equations away from the support of measure data
We prove boundedness and continuity for solutions to the Dirichlet problem for the equation where the left-hand side is a Leray-Lions operator from into with , is a Carathéodory function which grows like and is a finite Radon measure. We prove that renormalized solutions, though not globally bounded, are Hölder-continuous far from the support of .
Regularity properties of optimal transportation problems arising in hedonic pricing models
We study a form of optimal transportation surplus functions which arise in hedonic pricing models. We derive a formula for the Ma–Trudinger–Wang curvature of these functions, yielding necessary and sufficient conditions for them to satisfy (A3w). We use this to give explicit new examples of surplus functions satisfying (A3w), of the form b(x,y) = H(x + y) where H is a convex function on ℝn. We also show that the distribution of equilibrium contracts in this hedonic pricing model is absolutely continuous...
Remarks relevant to classical maximum principles.
Removable singularities for Hölder continuous quasiregular mappings in the plane.
Removable singularities for weak solutions of quasilinear elliptic systems.
Representation formulas for L∞ norms of weakly convergent sequences of gradient fields in homogenization
We examine the composition of the L∞ norm with weakly convergent sequences of gradient fields associated with the homogenization of second order divergence form partial differential equations with measurable coefficients. Here the sequences of coefficients are chosen to model heterogeneous media and are piecewise constant and highly oscillatory. We identify local representation formulas that in the fine phase limit provide upper bounds on the limit superior of the L∞ norms of gradient fields. The...
Representation formulas for L∞ norms of weakly convergent sequences of gradient fields in homogenization
We examine the composition of the L∞ norm with weakly convergent sequences of gradient fields associated with the homogenization of second order divergence form partial differential equations with measurable coefficients. Here the sequences of coefficients are chosen to model heterogeneous media and are piecewise constant and highly oscillatory. We identify local representation formulas that in the fine phase limit provide upper bounds on the limit...
Risultati di esistenza, regolarità e confronto per equazioni ellittiche
Schauder theorems for linear elliptic and parabolic problems with unbounded coefficients in
We study existence, uniqueness, and smoothing properties of the solutions to a class of linear second order elliptic and parabolic differential equations with unbounded coefficients in . The main results are global Schauder estimates, which hold in spite of the unboundedness of the coefficients.