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

Abstract

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Let F be a relatively closed subset of a Euclidean domain Ω . We investigate when solutions u to certain elliptic equations on Ω F are restrictions of solutions on all of Ω . Specifically, we show that if F is not too large, and u has a suitable decay rate near F , then u can be so extended.

How to cite

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Buckley, 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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  1. Falconer K.J., Geometry of Fractal Sets, Cambridge Univ. Press, Cambridge, 1985. Zbl0587.28004MR0867284
  2. Heinonen J., Kilpeläinen T., Martio O., Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Univ. Press, Oxford, 1993. MR1207810
  3. Kilpeläinen T., A Radó type theorem for p -harmonic functions in the plane, Electr. J. Diff. Eqns. 9 (1994), electronic. (1994) MR1303907
  4. Kilpeläinen T., Koskela P., Martio O., On the fusion problem for degenerate elliptic equations, Comm. P.D.E. 20 (1995), 485-497. (1995) MR1318078
  5. Koskela P., Martio O., Removability theorems for solutions of degenerate elliptic partial differential equations, Ark. Mat. 31 (1993), 339-353. (1993) Zbl0845.35015MR1263558
  6. Král J., Some extension results concerning harmonic functions, J. London Math. Soc. 28 (1983), 62-70. (1983) MR0703465
  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. Zbl0265.35019MR0393783

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