Radial Averaging Transformations and Generalized Capacities.
Radial Limits and growths of fractional Cauchy transforms
Radial limits of superharmonic functions in the plane
Radial variation of functions in Besov spaces.
Ray sequences of Laurent-type rational functions.
Rectifiability, analytic capacity, and singular integrals.
Reflected double layer potentials and Cauchy's operators
Necessary and sufficient conditions are given for the reflected Cauchy's operator (the reflected double layer potential operator) to be continuous as an operator from the space of all continuous functions on the boundary of the investigated domain to the space of all holomorphic functions on this domain (to the space of all harmonic functions on this domain) equipped with the topology of locally uniform convergence.
Reflection and a mixed boundary value problem concerning analytic functions
A mixed boundary value problem on a doubly connected domain in the complex plane is investigated. The solution is given in an integral form using reflection mapping. The reflection mapping makes it possible to reduce the problem to an integral equation considered only on a part of the boundary of the domain.
Reflection and the Dirichlet problem on doubly connected regions
Reflection and the Neumann problem on doubly connected regions
Regularity of The Complex Monge-Ampere Equation for Radially Symmetric Functions of the Unit Ball.
Remarks on equilibrium potential and energy
This note discusses to problem of the minimization of energy by the equilibrium measure obtained by the method of last exit in reference Ann. Inst. Fourier, 23-3 (1973), 313–322.
Removability of the wave singularities in the plane.
Removability of the wave singularities in the plane. (Summary).
Removable sets for Lipschitz harmonic functions in the plane.
The main motivation for this work comes from the century-old Painlevé problem: try to characterize geometrically removable sets for bounded analytic functions in C.
Réseaux électrique planaires I.
Reseaux électriques planaires II.
Retour sur la théorie de Littlewood-Paley
Riesz-Martin representation for positive super-polyharmonic functions in a Riemannian manifold.
Rotation-free solutions with positive infimum of the equation ...u = Pu in a neighbourhood of a singularity of the density P.