Results 1  10
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837
AN ASYMPTOTIC MEAN VALUE CHARACTERIZATION FOR pHARMONIC FUNCTIONS
"... Abstract. We characterize pharmonic functions in terms of an asymptotic mean value property. A pharmonic function u is a viscosity solution to ∆pu = div(∇up−2∇u) = 0 with 1 < p ≤ ∞ in a domain Ω if and only if the expansion u(x) = α 2 max ..."
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Cited by 29 (13 self)
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Abstract. We characterize pharmonic functions in terms of an asymptotic mean value property. A pharmonic function u is a viscosity solution to ∆pu = div(∇up−2∇u) = 0 with 1 < p ≤ ∞ in a domain Ω if and only if the expansion u(x) = α 2 max
On periodic pharmonic functions on Cayley tree.
, 803
"... Abstract: We show that any periodic with respect to normal subgroups (of the group representation of the Cayley tree) of finite index pharmonic function is a constant. For some normal subgroups of infinite index we describe a class of (nonconstant) periodic pharmonic functions. If p = 2, the ph ..."
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Cited by 2 (2 self)
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Abstract: We show that any periodic with respect to normal subgroups (of the group representation of the Cayley tree) of finite index pharmonic function is a constant. For some normal subgroups of infinite index we describe a class of (nonconstant) periodic pharmonic functions. If p = 2, the pharmonicity
THREE SPHERES THEOREM FOR pHARMONIC FUNCTIONS
, 2007
"... Abstract. Three spheres type theorem is proved for the pharmonic functions defined on the complement of kballs in the Euclidean ndimensional space. 1. ..."
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Cited by 4 (1 self)
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Abstract. Three spheres type theorem is proved for the pharmonic functions defined on the complement of kballs in the Euclidean ndimensional space. 1.
DIFFERENTIABILITY OF pHARMONIC FUNCTIONS ON METRIC MEASURE SPACES
"... Abstract. We study pharmonic functions on metric measure spaces, which are formulated as minimizers to certain energy functionals. For spaces supporting a pPoincaré inequality, we show that such functions satisfy an infinitesmal Lipschitz condition almost everywhere. This result is essentially sha ..."
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Abstract. We study pharmonic functions on metric measure spaces, which are formulated as minimizers to certain energy functionals. For spaces supporting a pPoincaré inequality, we show that such functions satisfy an infinitesmal Lipschitz condition almost everywhere. This result is essentially
A strong Liouville theorem for pharmonic functions on graphs
 Ann. Acad. Sci. Fen
, 1997
"... Abstract. We prove a global Harnack inequality for positive p harmonic functions on a graph Γ provided a weak Poincaré inequality holds on Γ and the counting measure of Γ is doubling. Consequently, every positive p harmonic function on such a graph must be constant. ..."
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Cited by 29 (1 self)
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Abstract. We prove a global Harnack inequality for positive p harmonic functions on a graph Γ provided a weak Poincaré inequality holds on Γ and the counting measure of Γ is doubling. Consequently, every positive p harmonic function on such a graph must be constant.
LOCAL GRADIENT ESTIMATE FOR pHARMONIC FUNCTIONS ON RIEMANNIAN MANIFOLDS
"... Abstract. For positive pharmonic functions on Riemannian manifolds, we derive a gradient estimate and Harnack inequality with constants depending only on the lower bound of the Ricci curvature, the dimension n, p and the radius of the ball on which the function is de…ned. Our approach is based on ..."
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Cited by 4 (1 self)
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Abstract. For positive pharmonic functions on Riemannian manifolds, we derive a gradient estimate and Harnack inequality with constants depending only on the lower bound of the Ricci curvature, the dimension n, p and the radius of the ball on which the function is de…ned. Our approach is based
REPR,ESENTATION OF A P.HARMONIC FUNCTION NEAR AN ISOLATED SINGULARITY IN THE PLANE
"... Abstract. A representation theorem is proved for a pharmonic function ( 1 < p < oo) near an isolated singularity in the plane. The proof uses stream functions and the hodograph method. The singularities can be classified as removable, poles and essential as is the case for analytic functions. ..."
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Abstract. A representation theorem is proved for a pharmonic function ( 1 < p < oo) near an isolated singularity in the plane. The proof uses stream functions and the hodograph method. The singularities can be classified as removable, poles and essential as is the case for analytic functions
MAXIMUM PRINCIPLE AND COMPARISON PRINCIPLE OF pHARMONIC FUNCTIONS VIA pHARMONIC BOUNDARY OF GRAPHS
"... Abstract. We prove the maximum principle and the comparison principle of pharmonic functions via pharmonic boundary of graphs. By applying the comparison principle, we also prove the solvability of the boundary value problem of pharmonic functions via pharmonic boundary of graphs. 1. ..."
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Abstract. We prove the maximum principle and the comparison principle of pharmonic functions via pharmonic boundary of graphs. By applying the comparison principle, we also prove the solvability of the boundary value problem of pharmonic functions via pharmonic boundary of graphs. 1.
A REGULARITY PROPERTY OF pHARMONIC FUNCTIONS
"... Abstract. The paper is concerned with the Aharmonic equation div[〈G(x)∇u,∇u〉(p−2)/2G(x)∇u] = 0 where 1 < p < ∞ and G is a positive definite matrix whose entries are in L ∞ ∩VMO. We show that for every r> 1, very weak solutions of class W 1,rloc actually belong to W 1,p loc and are solutio ..."
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Abstract. The paper is concerned with the Aharmonic equation div[〈G(x)∇u,∇u〉(p−2)/2G(x)∇u] = 0 where 1 < p < ∞ and G is a positive definite matrix whose entries are in L ∞ ∩VMO. We show that for every r> 1, very weak solutions of class W 1,rloc actually belong to W 1,p loc
Results 1  10
of
837