For the operator (−∆)^ν, the heat kernel is a generalized exponential (Fox-Wright) function E_{ν,d/2}(−x^2/4τ^{1/ν}), with power-law asymptotics for noninteger ν and oscillatory exponential asymptotics for integer ν.
Heat kernel estimates for the fractional Laplacian with Dirichlet conditions
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abstract
We give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet condition for a general class of domains including Lipschitz domains.
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hep-th 1years
2019 1verdicts
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Heat kernel for higher-order differential operators and generalized exponential functions
For the operator (−∆)^ν, the heat kernel is a generalized exponential (Fox-Wright) function E_{ν,d/2}(−x^2/4τ^{1/ν}), with power-law asymptotics for noninteger ν and oscillatory exponential asymptotics for integer ν.