TY - JOUR
T1 - Upper bounds for fundamental solutions to non-local diffusion equations with divergence free drift
AU - Maekawa, Yasunori
AU - Miura, Hideyuki
PY - 2013/5/15
Y1 - 2013/5/15
N2 - We consider some non-local diffusion equations in the presence of a divergence free drift term, where the diffusion operators are related to certain Dirichlet forms of jump type. We derive pointwise upper bounds for fundamental solutions of the equations under weak assumptions for the velocity of the drift term. Our class of the velocity includes functions with the scale-critical regularity and some growing functions at spatial infinity.
AB - We consider some non-local diffusion equations in the presence of a divergence free drift term, where the diffusion operators are related to certain Dirichlet forms of jump type. We derive pointwise upper bounds for fundamental solutions of the equations under weak assumptions for the velocity of the drift term. Our class of the velocity includes functions with the scale-critical regularity and some growing functions at spatial infinity.
KW - Divergence free drift
KW - Fundamental solutions
KW - Non-local diffusion
KW - Pointwise upper bound
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U2 - 10.1016/j.jfa.2013.02.011
DO - 10.1016/j.jfa.2013.02.011
M3 - Article
AN - SCOPUS:84875621379
VL - 264
SP - 2245
EP - 2268
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 10
ER -