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Generalization of weierstrass canonical integrals

Olga Veselovska (2004)

Open Mathematics

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

Jacqueline Ferrand (1998/1999)

Séminaire de théorie spectrale et géométrie

Generalized derivatives of an arbitrary order and the boundary properties of differentiated Poisson integrals for the half-space $ℝ_{+}^{k + 1}$ $(k > 1)$ .

Topuria, S. (2000)

Georgian Mathematical Journal

Generalized dirichlet problem in nonlinear potential theory.

Tero Kilpeläinen, Jan Maly (1990)

Manuscripta mathematica

Generalized Robin problem in potential theory

Ivan Netuka (1972)

Czechoslovak Mathematical Journal

Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential

Darko Žubrinić (2003)

Czechoslovak Mathematical Journal

We consider a quasilinear elliptic problem whose left-hand side is a Leray-Lions operator of $p$ -Laplacian type. If $p < γ < N$ and the right-hand side is a Radon measure with singularity of order $γ$ at $x_{0} \in Ω$ , then any supersolution in $W_{l o c}^{1, p} (Ω)$ has singularity of order at least $\frac{(γ - p)}{(p - 1)}$ at $x_{0}$ . In the proof we exploit a pointwise estimate of $𝒜$ -superharmonic solutions, due to Kilpeläinen and Malý, which involves Wolff’s potential of Radon’s measure.

Generators of the Space of Bounded Biharmonic Functions.

Leo Sario, Cecilia Wang (1972)

Mathematische Zeitschrift

Global higher integrability of jacobians on bounded domains

Jeff Hogan, Chun Li, Alan McIntosh, Kewei Zhang (2000)

Annales de l'I.H.P. Analyse non linéaire

Gradient potential estimates

Giuseppe Mingione (2011)

Journal of the European Mathematical Society

Pointwise gradient bounds via Riesz potentials like those available for the Poisson equation actually hold for general quasilinear equations.

Greenian Potentials and Concavity.

Christer Borell (1985)

Mathematische Annalen

Growth and asymptotic sets of subharmonic functions (II)

Jang-Mei Wu (1998)

Publicacions Matemàtiques

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 properties of spherical means for monotone BLD functions in the unit ball.

Mizuta, Yoshihiro, Shimomura, Tetsu (2000)

Annales Academiae Scientiarum Fennicae. Mathematica

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