Is Biharmonic Operator m-accretive?

83 Views Asked by At

We have seen in "S. Zheng,Nonlinear Evolution Equations(Taylor & Francis, 2004)" that the laplace operator $\Delta$ is m-accretive. I wanted to ask whether biharmonic operator $\Delta^{2}$ is also m-accretive ? Where Domain of $\Delta^{2}$ is $H_{0}^{2}\cap H^{4}$ . Any citation or hints are appreciated. Thanks in advance. where m-accretive operator is defined as below. \ Let A be a linear operator defined in a Banach space $B, A : D(A) ⊂ B \rightarrow B$. If for any $x,y \in D(A)$ and any $ \lambda > 0$, $||x-y||_{B} \leq ||x − y + λ(Ax − Ay)||_{B}$, then A is said to be an accretive operator. Moreover, if A is a densely defined accretive operator, and I + A is surjective, i.e., $R(I + A) = B$, then A is said to be a maximal accretive operator, in short, m-accretive.