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Various notions of dissipativity for partial differential operators and their applications

After introducing the concept of functional dissipativity of the Dirichlet problem in a domain Ω

.) of commuting maximal dissipative operators. To obtain such estimates, we use double operator integrals

In the present paper we consider the Dirichlet problem for the second order differential operator E

) of functions of maximal dissipative operators. This representation in terms of double operator integrals

concerning the Lp-dissipativity of scalar and matrix partial differential operators. In the second part we

for functions of contractions, dissipative operators, unitary operators and self-adjoint operators. To establish

with the high accuracy for the given dissipative problems.

The L^p-dissipativity of certain differential and integral operators

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