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- W2487919015 abstract "Let $c_{kl} in W^{2,infty}(mathbb{R}^d, mathbb{C})$ for all $k,l in {1, ldots, d}$. We consider the divergence form operator $A = - sum_{k,l=1}^d partial_l (c_{kl} , partial_k) $in $L_2(mathbb{R}^d)$ when the coefficient matrix satisfies $(C(x) , xi, xi) in Sigma_theta$ for all $x in mathbb{R}^d$ and $xi in mathbb{C}^d$, where $Sigma_theta$ be the sector with vertex 0 and semi-angle $theta$ in the complex plane. We show that for all $p$ in a suitable interval the contraction semigroup generated by $-A$ extends consistently to a contraction semigroup on $L_p(mathbb{R}^d)$. For those values of $p$ we present a condition on the coefficients such that the space $C_c^infty(mathbb{R}^d)$ of test functions is a core for the generator on $L_p(mathbb{R}^d)$. We also examine the operator $A$ separately in the more special Hilbert space $L_2(mathbb{R}^d)$ setting and provide more sufficient conditions such that $C_c^infty(mathbb{R}^d)$ is a core." @default.
- W2487919015 created "2016-08-23" @default.
- W2487919015 creator A5000712400 @default.
- W2487919015 date "2016-07-23" @default.
- W2487919015 modified "2023-09-27" @default.
- W2487919015 title "Degenerate elliptic operators in $L_p$-spaces with complex $W^{2,infty}$-coefficients" @default.
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- W2487919015 hasPublicationYear "2016" @default.
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