# Optimal estimates for derivatives of analytic functions and solutions to Laplace, Lam\'e and Stokes equations

יום ב', 19/05/2014 - 14:00
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Abstract:

Two types of optimal estimates for derivatives of analytic functions
with bounded real part are considered. The first of them is a pointwise
inequality for derivatives of analytic functions in the complement
of a convex closed domain in \${\mathbb C}\$. The second type of inequalities
is a limit relation for derivatives of analytic functions in an arbitrary proper
subdomain of \${\mathbb C}\$. Optimal estimates for derivatives of a vector
field with bounded harmonic components as well as optimal estimates for the
divergence of an elastic displacement field and pressure in a fluid in
subdomains of \${\mathbb R}^n\$ are discussed.