| Title:
|
Removability of singularities with anisotropic growth (English) |
| Author:
|
Dont, Miroslav |
| Author:
|
Král, Josef, Jr. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
128 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
1-19 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
With help of suitable anisotropic Minkowski’s contents and Hausdorff measures some results are obtained concerning removability of singularities for solutions of partial differential equations with anisotropic growth in the vicinity of the singular set. (English) |
| Keyword:
|
solutions of partial differential equations |
| Keyword:
|
removable singularities |
| Keyword:
|
anisotropic metric |
| Keyword:
|
Minkowski’s contents |
| MSC:
|
28A12 |
| MSC:
|
35A20 |
| MSC:
|
35B05 |
| MSC:
|
35B60 |
| MSC:
|
35J30 |
| MSC:
|
65Z05 |
| idZBL:
|
Zbl 1015.35003 |
| idMR:
|
MR1973420 |
| DOI:
|
10.21136/MB.2003.133932 |
| . |
| Date available:
|
2009-09-24T22:06:18Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133932 |
| . |
| Reference:
|
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| Reference:
|
[2] M. de Guzmán: Differentitation of Integrals in $\mathbb{R}^n$.Springer, Berlin, 1975. MR 0457661 |
| Reference:
|
[3] S. Fučík, O. John, A. Kufner: Function Spaces I.SPN, Praha, 1974. (Czech) |
| Reference:
|
[4] R. Harvey, J. Polking: Removable singularities of solutions of linear partial differential equations.Acta Mathematica 125 (1970), 39–56. MR 0279461, 10.1007/BF02838327 |
| Reference:
|
[5] P. Koskela: Removable singularities for analytic functions.Michigan Math. J. 40 (1993), 459–466. Zbl 0805.30001, MR 1236172, 10.1307/mmj/1029004831 |
| Reference:
|
[6] J. Král: Removability of singularities in potential theory.Potential Analysis 3 (1994), 119–131. MR 1266221, 10.1007/BF01047839 |
| Reference:
|
[7] J. Král, Jr.: Removable singularities for harmonic and caloric functions.Thesis, FJFI ČVUT, Praha, 1999. (Czech) |
| Reference:
|
[8] W. Littman: Polar sets and removable singularities of partial differential equations.Ark. Mat. 7 (1967), 1–9. Zbl 0158.11004, MR 0224960, 10.1007/BF02591673 |
| Reference:
|
[9] O. Martio, M. Vuorinen: Whitney cubes, $p$-capacity and Minkowski content.Expo. Math. 5 (1987), 17–40. MR 0880256 |
| Reference:
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[10] M. Píštěk: Removable singularities of solutions of partial differential equations.Thesis, MFF UK, Praha, 1993. (Czech) |
| Reference:
|
[11] J. C. Polking: A survey of removable singularities.Seminar Nonlinear Partial Differential Equations, New York, 1987, pp. 261–292. MR 0765238 |
| Reference:
|
[12] M. Sugimoto, M. Uchida: A generalization of Bochner’s extension theorem and its application.Ark. Mat. 38 (2000), 399–409. MR 1785409, 10.1007/BF02384327 |
| Reference:
|
[13] N. N. Tarkhanov: The Analysis of Solutions of Elliptic Equations.Kluver Academic Publishers, 1997. Zbl 0877.35002, MR 1447439 |
| Reference:
|
[14] J. F. Trèves: Lectures on Linear Partial Differential Equations with Constant Coefficients.Rio de Janeiro, 1961. MR 0155078 |
| Reference:
|
[15] H. Zlonická: Singularity of solutions of partial differential equations.Thesis, MFF UK, Praha, 1984. (Czech) |
| . |
