On the fusion problem for degenerate elliptic equations II
Stephen M. Buckley; Pekka Koskela
Commentationes Mathematicae Universitatis Carolinae (1999)
- Volume: 40, Issue: 1, page 1-6
- ISSN: 0010-2628
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topBuckley, Stephen M., and Koskela, Pekka. "On the fusion problem for degenerate elliptic equations II." Commentationes Mathematicae Universitatis Carolinae 40.1 (1999): 1-6. <http://eudml.org/doc/248427>.
@article{Buckley1999,
abstract = {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.},
author = {Buckley, Stephen M., Koskela, Pekka},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\mathcal \{A\}$-harmonic function; Hausdorff measure; Fusion problem; -harmonic function; Hausdorff measure; fusion problem},
language = {eng},
number = {1},
pages = {1-6},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the fusion problem for degenerate elliptic equations II},
url = {http://eudml.org/doc/248427},
volume = {40},
year = {1999},
}
TY - JOUR
AU - Buckley, Stephen M.
AU - Koskela, Pekka
TI - On the fusion problem for degenerate elliptic equations II
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 1
SP - 1
EP - 6
AB - 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.
LA - eng
KW - $\mathcal {A}$-harmonic function; Hausdorff measure; Fusion problem; -harmonic function; Hausdorff measure; fusion problem
UR - http://eudml.org/doc/248427
ER -
References
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- Král J., Some extension results concerning harmonic functions, J. London Math. Soc. 28 (1983), 62-70. (1983) MR0703465
- 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. Zbl0265.35019MR0393783
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