| Title:
|
On a conjecture of Král concerning the subharmonic extension of continuously differentiable functions (English) |
| Author:
|
Gardiner, Stephen J. |
| Author:
|
Sjödin, Tomas |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
145 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
71-73 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This note verifies a conjecture of Král, that a continuously differentiable function, which is subharmonic outside its critical set, is subharmonic everywhere. (English) |
| Keyword:
|
subharmonic function |
| Keyword:
|
extension theorem |
| MSC:
|
31B05 |
| idZBL:
|
07217181 |
| idMR:
|
MR4088694 |
| DOI:
|
10.21136/MB.2019.0104-18 |
| . |
| Date available:
|
2020-03-12T08:20:33Z |
| Last updated:
|
2020-11-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148065 |
| . |
| Reference:
|
[1] Armitage, D. H., Gardiner, S. J.: Classical Potential Theory.Springer Monographs in Mathematics. Springer, London (2001). Zbl 0972.31001, MR 1801253, 10.1007/978-1-4471-0233-5 |
| Reference:
|
[2] Caffarelli, L. A., Cabré, X.: Fully Nonlinear Elliptic Equations.Colloquium Publications 43. AMS, Providence (1995). Zbl 0834.35002, MR 1351007, 10.1090/coll/043 |
| Reference:
|
[3] Crandall, M. G., Ishii, H., Lions, P.-L.: User's guide to viscosity solutions of second order partial differential equations.Bull. Am. Math. Soc., New Ser. 27 (1992), 1-67. Zbl 0755.35015, MR 1118699, 10.1090/S0273-0979-1992-00266-5 |
| Reference:
|
[4] Juutinen, P., Lindqvist, P.: A theorem of Radó's type for the solutions of a quasi-linear equation.Math. Res. Lett. 11 (2004), 31-34. Zbl 1153.35324, MR 2046197, 10.4310/MRL.2004.v11.n1.a4 |
| Reference:
|
[5] Juutinen, P., Lindqvist, P., Manfredi, J. J.: On the equivalence of viscosity solutions and weak solutions for a quasi-linear equation.SIAM J. Math. Anal. 33 (2001), 699-717. Zbl 0997.35022, MR 1871417, 10.1137/S0036141000372179 |
| Reference:
|
[6] Král, J.: Some extension results concerning harmonic functions.J. Lond. Math. Soc., II. Ser. 28 (1983), 62-70. Zbl 0526.31003, MR 0703465, 10.1112/jlms/s2-28.1.62 |
| Reference:
|
[7] Král, J.: A conjecture concerning subharmonic functions.Čas. Pěst. Mat. 110 (1985), page 415 Czech. 10.21136/CPM.1985.118241 |
| Reference:
|
[8] Pokrovskiĭ, A. V.: A simple proof of the Radó and Král theorems on removability of the zero locus for analytic and harmonic functions.Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2015 (2015), 29-31. Zbl 1340.30135, MR 3718287, 10.15407/dopovidi2015.07.029 |
| Reference:
|
[9] Rudin, W.: Real and Complex Analysis.McGraw-Hill Book Co., New York (1987). Zbl 0925.00005, MR 0924157 |
| . |
