| Title:
|
On the fusion problem for degenerate elliptic equations II (English) |
| Author:
|
Buckley, Stephen M. |
| Author:
|
Koskela, Pekka |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
1-6 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $F$ be a relatively closed subset of a Euclidean domain $\Omega$. We investigate when solutions $u$ to certain elliptic equations on $\Omega\setminus F$ are restrictions of solutions on all of $\Omega$. Specifically, we show that if $\partial F$ is not too large, and $u$ has a suitable decay rate near $F$, then $u$ can be so extended. (English) |
| Keyword:
|
$\Cal A$-harmonic function |
| Keyword:
|
Hausdorff measure |
| Keyword:
|
Fusion problem |
| MSC:
|
28A78 |
| MSC:
|
35J60 |
| MSC:
|
35J70 |
| idZBL:
|
Zbl 1060.35511 |
| idMR:
|
MR1715198 |
| . |
| Date available:
|
2009-01-08T18:49:10Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119059 |
| . |
| Reference:
|
[1] Falconer K.J.: Geometry of Fractal Sets.Cambridge Univ. Press, Cambridge, 1985. Zbl 0587.28004, MR 0867284 |
| Reference:
|
[2] Heinonen J., Kilpeläinen T., Martio O.: Nonlinear Potential Theory of Degenerate Elliptic Equations.Oxford Univ. Press, Oxford, 1993. MR 1207810 |
| Reference:
|
[3] Kilpeläinen T.: A Radó type theorem for $p$-harmonic functions in the plane.Electr. J. Diff. Eqns. 9 (1994), electronic. MR 1303907 |
| Reference:
|
[4] Kilpeläinen T., Koskela P., Martio O.: On the fusion problem for degenerate elliptic equations.Comm. P.D.E. 20 (1995), 485-497. MR 1318078 |
| Reference:
|
[5] Koskela P., Martio O.: Removability theorems for solutions of degenerate elliptic partial differential equations.Ark. Mat. 31 (1993), 339-353. Zbl 0845.35015, MR 1263558 |
| Reference:
|
[6] Král J.: Some extension results concerning harmonic functions.J. London Math. Soc. 28 (1983), 62-70. MR 0703465 |
| Reference:
|
[7] Miller K.: Non-unique continuation for certain ODE's in Hilbert space and for uniformly parabolic and elliptic equations in self-adjoint divergence form.in Symposium on non-well-posed problems and logarithmic convexity, ed. R.J. Knops, Lecture Notes in Math. 316, pp.85-101, Springer-Verlag, Berlin, 1973. Zbl 0265.35019, MR 0393783 |
| . |
