TY - JOUR
T1 - Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces
AU - Kuwae, Kazuhiro
AU - Machigashira, Yoshiroh
AU - Shioya, Takashi
PY - 2001/10/1
Y1 - 2001/10/1
N2 - We prove the compactness of the imbedding of the Sobolev space W1,20 (Ω) into L2 (Ω) for any relatively compact open subset Ω of an Alexandrov space. As a corollary, the generator induced from the Dirichlet (energy) form has discrete spectrum. The generator can be approximated by the Laplacian induced from the DC-structure on the Alexandrov space. We also prove the existence of the locally Hölder continuous heat kernel.
AB - We prove the compactness of the imbedding of the Sobolev space W1,20 (Ω) into L2 (Ω) for any relatively compact open subset Ω of an Alexandrov space. As a corollary, the generator induced from the Dirichlet (energy) form has discrete spectrum. The generator can be approximated by the Laplacian induced from the DC-structure on the Alexandrov space. We also prove the existence of the locally Hölder continuous heat kernel.
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U2 - 10.1007/s002090100252
DO - 10.1007/s002090100252
M3 - Article
AN - SCOPUS:0035639753
VL - 238
SP - 269
EP - 316
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 2
ER -