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On a direct decomposition of the space $ℒ_{p} (Ω)$ .

Kähler, U. (1999)

Zeitschrift für Analysis und ihre Anwendungen

On a maximum principle in potential theory

Dagmar Medková (1982)

Časopis pro pěstování matematiky

On Hardy type inequality with non-isotropic kernels.

Sarikaya, Mehmet Zeki, Yildrim, Hüseyin (2006)

Lobachevskii Journal of Mathematics

On integrals of harmonic functions over annuli.

Korenblum, B., Rippon, P.J., Samotij, K. (1995)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

On parameter differentiation for integral representations of associated Legendre functions.

Cohl, Howard S. (2011)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

On some problems of Choquet theory connected with potential theory

Kesel'man, D. G. (1984)

Proceedings of the 12th Winter School on Abstract Analysis

On the boundary limits of harmonic functions with gradient in $L^{p}$

Yoshihiro Mizuta (1984)

Annales de l'institut Fourier

This paper deals with tangential boundary behaviors of harmonic functions with gradient in Lebesgue classes. Our aim is to extend a recent result of Cruzeiro (C.R.A.S., Paris, 294 (1982), 71–74), concerning tangential boundary limits of harmonic functions with gradient in $L^{n} (R_{+}^{n})$ , $R_{+}^{n}$ denoting the upper half space of the $n$ -dimensional euclidean space $R^{n}$ . Our method used here is different from that of Nagel, Rudin and Shapiro (Ann. of Math., 116 (1982), 331–360); in fact, we use the integral representation...

On the Cauchy Problem for the Kadomstev-Petviashvili Equation.

J. Bourgain (1993)

Geometric and functional analysis

On the existence of steady-state solutions to the Navier-Stokes system for large fluxes

Antonio Russo, Giulio Starita (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper we deal with the stationary Navier-Stokes problem in a domain $Ω$ with compact Lipschitz boundary $\partial Ω$ and datum $a$ in Lebesgue spaces. We prove existence of a solution for arbitrary values of the fluxes through the connected components of $\partial Ω$ , with possible countable exceptional set, provided $a$ is the sum of the gradient of a harmonic function and a sufficiently small field, with zero total flux for $Ω$ bounded.

On the $(p, q)$ -boundedness of nonisotropic spherical Riesz potentials.

Sarikaya, Mehmet Zeki, Yildirim, Hüseyin (2007)

Journal of Inequalities and Applications [electronic only]

On the potential theory of some systems of coupled PDEs

Abderrahim Aslimani, Imad El Ghazi, Mohamed El Kadiri, Sabah Haddad (2016)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study some potential theoretical properties of solutions and super-solutions of some PDE systems (S) of type $L_{1} u = - μ_{1} v$ , $L_{2} v = - μ_{2} u$ , on a domain $D$ of $ℝ^{d}$ , where $μ_{1}$ and $μ_{2}$ are suitable measures on $D$ , and $L_{1}$ , $L_{2}$ are two second order linear differential elliptic operators on $D$ with coefficients of class $𝒞^{\infty}$ . We also obtain the integral representation of the nonnegative solutions and supersolutions of the system (S) by means of the Green kernels and Martin boundaries associated with $L_{1}$ and $L_{2}$ , and a convergence...

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