On scale invariant bounds for Green's function for second order elliptic equations with lower order coefficients and applications.

@inproceedings{Sakellaris2019OnSI,
  title={On scale invariant bounds for Green's function for second order elliptic equations with lower order coefficients and applications.},
  author={Georgios Sakellaris},
  year={2019}
}
We construct Green's functions for elliptic operators of the form $\mathcal{L}u=-\text{div}(A\nabla u+bu)+c\nabla u+du$ in domains $\Omega\subseteq\mathbb R^n$, under the assumption $d\geq\text{div}b$, or $d\geq\text{div}c$. We show that, in the setting of Lorentz spaces, the assumption $b-c\in L^{n,1}(\Omega)$ is both necessary and optimal to obtain pointwise bounds for Green's functions. We also show weak type bounds for Green's functions and their gradients. Our estimates are scale invariant… CONTINUE READING

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