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- W2952769234 abstract "Let $Dsubset R^d$ be a bounded domain and let [ L=frac12nablacdot anabla +bcdotnabla ] %[ %L=frac12sum_{i,j=1}^da_{i,j}frac{partial^2}{partial x_ipartial x_j}+sum_{i=1}^db_ifrac{partial}{partial x_i}, %] be a second order elliptic operator on $D$. Let $nu$ be a probability measure on $D$. Denote by ${mathcal L}$ the differential operator whose domain is specified by the following non-local boundary condition: $$ {mathcal D_{{mathcal L}}}={fin C^2(ol{D}): int_D f dnu = f|_{partial D}}, $$ and which coincides with $L$ on its domain. It is known that $mathcal L$ possesses an infinite sequence of eigenvalues, and that with the exception of the zero eigenvalue, all eigenvalues have negative real part. Define the spectral gap of $mathcal {L}$, indexed by $nu$, by gamma_1(nu)equivsup{re lambda:0neq lambda is an eigenvalue for {mathcal L}}. In this paper we investigate the eigenvalues of $mathcal L$ in general and the spectral gap $gamma_1(nu)$ in particular. The operator $mathcal L$ is the generator of a diffusion process with random jumps from the boundary, and $gamma_1(nu)$ measures the exponential rate of convergence of this process to its invariant measure." @default.
- W2952769234 created "2019-06-27" @default.
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- W2952769234 date "2007-07-04" @default.
- W2952769234 modified "2023-09-27" @default.
- W2952769234 title "Spectral Analysis of a Family of Second-Order Elliptic Operators with Nonlocal Boundary Condition Indexed by a Probabilty Measure" @default.
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