Hardy inequalities for weighted Dirac operatos

Details Hardy inequalities for weighted Dirac operatos Hardy inequalities for weighted Dirac operatos

2008-12-15

arxiv.org/abs/0812.2778v1

Mathematics

Analysis of PDEs

Scientific paper

An inequality of Hardy type is established for quadratic forms involving Dirac operator and a weight $r^{-b}$ for functions in $\R^n$. The exact Hardy constant $c_b=c_b(n)$ is found and generalized minimizers are given. The constant $c_b$ vanishes on a countable set of $b$, which extends the known case $n=2$, $b=0$ which corresponds to the trivial Hardy inequality in $\R^2$. Analogous inequalities are proved in the case $c_b=0$ under constraints and, with error terms, for a bounded domain.

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