# fa.useful evaluation – Reference Request: Dirichlet operators with eccentric coefficients retort

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## fa.useful evaluation – Reference Request: Dirichlet operators with eccentric coefficients

Let $$dgeq 2$$, $$delta in (0,1)$$ and let $$mathcal{L}_{d,delta}$$ breathe the second bid differential operator outlined by
commence{align*} mathcal{L}_{d,delta}(f)(x) = Delta(f)(x)-delta |x|^{delta-2}langle x;nabla(f)(x)rangle. stop{align*}
assume the feeble formulation downside in $$L^2(mu_delta)$$:
commence{align*} mathcal{L}_{d,delta}(f) = g stop{align*}
for some knowledge $$g in L^2(mu_delta)$$ such that
commence{align*} int_{mathbb{R}^d} g(x) mu_delta(dx) = int_{mathbb{R}^d} g(x) expleft(-|x|^{delta}capable) dx = 0. stop{align*}
What can breathe stated in regards to the resolution $$f$$ (if it exists) of such a feeble formulation downside? I’m in search of any references concerning this kindly of PDE with eccentric coefficients. level to that you do not maintain Poincaré inequality.

Thanks in close by.

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