General approach to regions of variability via subordination of harmonic mappings.
Generalization of weierstrass canonical integrals
In this paper we prove that a subharmonic function in ℝm of finite λ-type can be represented (within some subharmonic function) as the sum of a generalized Weierstrass canonical integral and a function of finite λ-type which tends to zero uniformly on compacts of ℝm. The known Brelot-Hadamard representation of subharmonic functions in ℝm of finite order can be obtained as a corollary from this result. Moreover, some properties of R-remainders of λ-admissible mass distributions are investigated.
Generalized condensers and conformal properties of riemannian manifolds with at least two ends
Generalized derivatives of an arbitrary order and the boundary properties of differentiated Poisson integrals for the half-space .
Generalized Dirac Operators on Nonsmooth Manifolds and Maxwell's Equations.
Generalized dirichlet problem in nonlinear potential theory.
Generalized Dirichlet Problems and Continuous Selections of Representing Measures.
Generalized Robin problem in potential theory
Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential
We consider a quasilinear elliptic problem whose left-hand side is a Leray-Lions operator of -Laplacian type. If and the right-hand side is a Radon measure with singularity of order at , then any supersolution in has singularity of order at least at . In the proof we exploit a pointwise estimate of -superharmonic solutions, due to Kilpeläinen and Malý, which involves Wolff’s potential of Radon’s measure.
Generators of the Space of Bounded Biharmonic Functions.
Geometry of compactifications of locally symmetric spaces
For a locally symmetric space , we define a compactification which we call the “geodesic compactification”. It is constructed by adding limit points in to certain geodesics in . The geodesic compactification arises in other contexts. Two general constructions of Gromov for an ideal boundary of a Riemannian manifold give for locally symmetric spaces. Moreover, has a natural group theoretic construction using the Tits building. The geodesic compactification plays two fundamental roles in...
Girsanov and Feynman–Kac type transformations for symmetric Markov processes
Global higher integrability of jacobians on bounded domains
Gradient potential estimates
Pointwise gradient bounds via Riesz potentials like those available for the Poisson equation actually hold for general quasilinear equations.
Green functions for killed random walks in the Weyl chamber of Sp(4)
We consider a family of random walks killed at the boundary of the Weyl chamber of the dual of Sp(4), which in addition satisfies the following property: for any n ≥ 3, there is in this family a walk associated with a reflection group of order 2n. Moreover, the case n = 4 corresponds to a process which appears naturally by studying quantum random walks on the dual of Sp(4). For all the processes belonging to this family, we find the exact asymptotic of the Green functions along all infinite paths...
Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel–Leader graphs
Greenian Potentials and Concavity.
Growth and asymptotic sets of subharmonic functions (II)
We study the relation between the growth of a subharmonic function in the half space Rn+1+ and the size of its asymptotic set. In particular, we prove that for any n ≥ 1 and 0 < α ≤ n, there exists a subharmonic function u in the Rn+1+ satisfying the growth condition of order α : u(x) ≤ x-αn+1 for 0 < xn+1 < 1, such that the Hausdorff dimension of the asymptotic set ∪λ≠0A(λ) is exactly n-α. Here A(λ) is the set of boundary points at which f tends to λ along some curve. This...
Growth of entire -subharmonic functions.
Growth properties of spherical means for monotone BLD functions in the unit ball.