On the strict concavity of the harmonic radius in dimension \(N\geq 3\)
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Publication:1606262
DOI10.1016/S0021-7824(01)01246-6zbMath1027.31003OpenAlexW2059287301MaRDI QIDQ1606262
Rabah Tahraoui, Pierre Cardaliaguet
Publication date: 24 July 2002
Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0021-7824(01)01246-6
Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Second-order elliptic equations (35J15) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)
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Cites Work
- Unnamed Item
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- Unnamed Item
- Capacitary inequalities of the Brunn-Minkowski type
- Hyperbolic metric, curvature of geodesics and hyperbolic discs in hyperbolic plane domains
- Univalence criteria and the hyperbolic metric
- Convexity of solutions of semilinear elliptic equations
- Capacitary functions in convex rings
- Asymptotic shape and location of small cores in elliptic free-boundary problems
- An asymptotic formula for the minimal capacity among sets of equal area
- Convex viscosity solutions and state constraints
- Concentration of low energy extremals: Identification of concentration points
- On the case of equality in the Brunn-Minkowski inequality for capacity
- The hyperbolic and quasihyperbolic metrics in convex regions
- Transplantation harmonique, transplantation par modules, et théoremes isoperimetriques
- On the convexity of a solution of Liouville's equation
- Sur la stricte concavité du rayon harmonique en dimension
- An Extended Principle of the Maximum for Harmonic Functions in 3-Dimensions
- A Result Concerning Convex Level Surfaces of 3-Dimensional Harmonic Functions
- Further Results Concerning the Level Surfaces of the Green's Function for a 3-Dimensional Convex Domain (I)
- Harmonic Radius and Concentration of Energy; Hyperbolic Radius and Liouville’s Equations $\Delta U = e^U $ and $\Delta U = U^{\tfrac{{n + 2}}{{n - 2}}} $
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