Regularity of the extremal solution of semilinear elliptic equations

By G. Nedev. 2000

142 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/5e7fdfe0f430438bc407909ba765942ac598b321

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Xavier Ros-Oton
2. J. Serra
3. X. Cabré
4. Yannick Sire
5. Enrico Valdinoci
6. M. Fall
7. Mostafa Fazly
8. J. D'avila

In Computational Theory and Mathematics

1. Xavier Ros-Oton
2. X. Cabré
3. J. Serra
4. Yannick Sire
5. M. Fall
6. J. D'avila
7. Enrico Valdinoci
8. Louis Dupaigne

Citations in the corpus

• Semi-stable and extremal solutions of reaction equations involving the $p$-Laplacian (2006, background): “[28] establishes the boundedness of the extremal solution wheneverN < p+p/(p−1), extending an important work of Nedev [26] for p = 2.”
• Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS (2010, background): “Nedev [138] showed that this is indeed the case for N D 3, while Cabré and Capella [36] have shown that this remains the case up to dimension N D 9 provided one is dealing with a radially symmetric case.”
• Boundedness of the extremal solution of some p-Laplacian problems (2007, background): “Its proof uses some of the arguments appearing in [20] and [21].”
• Stable solutions to semilinear elliptic equations are smooth up to dimension $9$ (2019, background): “In particular, partial positive answers to the conjecture above have been given (chronologically): • by Nedev, when n ≤ 3 [30]; • by Cabré and Capella when Ω = B1 and n ≤ 9 [10]; • by Cabré when n = 4 and Ω is convex [7] (see [9] for an alternative proof); • by Villegas when n = 4 [39]; • by Cabre”
• Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations (2010, background): “[23] Nedev, G. (2000).”
• Regularity of Stable Solutions up to Dimension 7 in Domains of Double Revolution (2012, methodology): “[12] G. Nedev, Regularity of the extremal solution of semilinear elliptic equations, C. R. Acad.”
• De Giorgi type results for elliptic systems (2012, result): “It is worth comparing to the general results of Nedev [14] and Cabré [8] regarding the regularity of stable solutions of semilinear equations with general nonlinearities up to dimension four.”
• The extremal solution of a boundary reaction problem (2008, background): “[23] G.”
• Regularity of minimizers of semilinear elliptic problems up to dimension 4 (2009, background): “(1.6) It is well known (see [2, 4, 6] and references therein) that there exists an extremal parameter λ∗ ∈ (0,∞) such that if 0 ≤ λ λ∗ then (1.5λ) admits a minimal classical solution uλ.”