PreprintFractional powers of monotone operators in Hilbert spacesDaniel Hauer, Yuan He, Dehui LiuAbstractIn this article, we show that for maximal monotone operators \(A\) on \(H\) with \(0\) in the range \(\textrm{Rg}(A)\) of \(A\) and every \(0 < \sigma\le 1/2\), the Dirichlet problem associated with the Besseltype equation \[ A_{12\sigma u}:=\frac{12\sigma} tu_tu_{tt}+Au\ni 0 \] is wellposed and the associated DirichlettoNeumann map \(\Lambda_{\sigma}\) is a maximal monotone operator on \(H\). This allows to defined fractional powers \(A^{\alpha}\) of nonlinear operators. Keywords: Monotone operators, Hilbert space, evolution equations, fractional operators.
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