TY - JOUR
T1 - A Wpn-theory of parabolic equations with unbounded leading coefficients on non-smooth domains
AU - Kim, Kyeong Hun
N1 - Funding Information:
✩ This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MEST) (No. R01-2008-000-20010-0). E-mail address: kyeonghun@korea.ac.kr.
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
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U2 - 10.1016/j.jmaa.2008.09.058
DO - 10.1016/j.jmaa.2008.09.058
M3 - Article
AN - SCOPUS:54149117987
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 -