Mathematics – Analysis of PDEs
Scientific paper
2009-10-29
Mathematics
Analysis of PDEs
13 pages, no figures
Scientific paper
Let $\Phi$ be a real valued function of one real variable, let $L$ denote an elliptic second order formally self-adjoint differential operator with bounded measurable coefficients, and let $P$ stand for the Poisson operator for $L$. A necessary and sufficient condition on $\Phi ensuring the equivalence of the Dirichlet integrals of $\Phi\circ Ph$ and $P(\Phi\circ h)$ is obtained. We illustrate this result by some sharp inequalities for harmonic functions.
Cialdea Alberto
Maz'ya Vladimir
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