Abstract
We study parabolic partial differential equations with unbounded second-, first- and zero-order coefficients on non-smooth domains allowing Hardy inequality. Existence and uniqueness results are given in weighted Sobolev spaces, and Hölder estimates of the solutions are also obtained. The number of derivatives of the solutions can be any nonnegative real number, in particular, it can be fractional.
| Original language | English |
|---|---|
| Pages (from-to) | 294-305 |
| Number of pages | 12 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 350 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2009 Feb 1 |
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Keywords
- Hardy inequality
- Non-smooth domains
- Unbounded leading coefficients
- Weighted Sobolev spaces
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
A Wp n-theory of parabolic equations with unbounded leading coefficients on non-smooth domains. / Kim, Kyeong Hun.
In: Journal of Mathematical Analysis and Applications, Vol. 350, No. 1, 01.02.2009, p. 294-305.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A Wp n-theory of parabolic equations with unbounded leading coefficients on non-smooth domains
AU - Kim, Kyeong Hun
PY - 2009/2/1
Y1 - 2009/2/1
N2 - We study parabolic partial differential equations with unbounded second-, first- and zero-order coefficients on non-smooth domains allowing Hardy inequality. Existence and uniqueness results are given in weighted Sobolev spaces, and Hölder estimates of the solutions are also obtained. The number of derivatives of the solutions can be any nonnegative real number, in particular, it can be fractional.
AB - We study parabolic partial differential equations with unbounded second-, first- and zero-order coefficients on non-smooth domains allowing Hardy inequality. Existence and uniqueness results are given in weighted Sobolev spaces, and Hölder estimates of the solutions are also obtained. The number of derivatives of the solutions can be any nonnegative real number, in particular, it can be fractional.
KW - Hardy inequality
KW - Non-smooth domains
KW - Unbounded leading coefficients
KW - Weighted Sobolev spaces
UR - http://www.scopus.com/inward/record.url?scp=54149117987&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=54149117987&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2008.09.058
DO - 10.1016/j.jmaa.2008.09.058
M3 - Article
VL - 350
SP - 294
EP - 305
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -