Refinement of an Lp-Estimate of Solonnikov for a Parabolic Equation of the Second Order with Conormal Boundary Condition.
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
Regular growth of subharmonic functions of several variables.
Regular potentials of additive functionals in semidynamical systems
We consider a semidynamical system . We introduce the cone of continuous additive functionals defined on and the cone of regular potentials. We define an order relation “” on and a specific order “” on . We will investigate the properties of and and we will establish the relationship between the two cones.
Regularity of a free boundary with application to the Pompeiu problem.
Regularity of p-harmonic functions on the plane.
Regularity of some nonlinear quantities on superharmonic functions in local Herz-type Hardy spaces.
In this paper, the authors introduce a kind of local Hardy spaces in Rn associated with the local Herz spaces. Then the authors investigate the regularity in these local Hardy spaces of some nonlinear quantities on superharmonic functions on R2. The main results of the authors extend the corresponding results of Evans and Müller in a recent paper.
Regularity of The Complex Monge-Ampere Equation for Radially Symmetric Functions of the Unit Ball.
Regularizing sets of irregular points.
Relative Fatou theorem for harmonic functions of rotation invariant stable processes in smooth domains
For domains we give exact asymptotics near the domain’s boundary for the Green function and Martin kernel of the rotation invariant α-stable Lévy process. We also obtain a relative Fatou theorem for harmonic functions of the stable process.
Relaxation for Dirichlet problems involving a Dirichlet form.
Remark on Ugaheri's maximum principle
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.
Remarks on Fine Continuity and the Base Operation in Potential Theory.
Remarks on pluripolar hulls
The aim of the paper is to establish some results on pluripolar hulls and to define pluripolar hulls of certain graphs.
Remarks on some fourth order variational inequalities
Remarks on subharmonic envelopes.
We prove that the subharmonic envelope of a lower semicontinuous function on Omega is harmonic on a certain open subset of Omega, using a very classical method in potential theory. The result gives simple proofs of theorems on harmonic measures and Jensen measures obtained by Cole and Ransford.