## On overdetermined Hardy inequalities.(English)Zbl 0936.26009

Let $$M_0$$ and $$M_1$$ be subsets of $$\{0,1,\ldots ,k-1\}$$ such that $$M_0 +M_1 >k$$, $$k\in \mathbb N$$. The paper is devoted to a characterization of the $$k$$-th order Hardy inequality $\Big (\int ^1_0 |u(x)|^q w_0(x)dx\Big)^{1/q} \leq C\Big (\int ^1_0 |u^{(k)} (x)|^pw(x)dx\Big)^{1/p},$ where $$w_0$$ and $$w$$ are weights, $$1<p<\infty$$, $$0<q<\infty$$, and $$u\in AC^{(k-1)} (0,1)$$ satisfies the “boundary” conditions $$u^{(i)} (0) = 0$$, $$i\in M_0$$, $$u^{(j)} (1) = 0$$, $$j\in M_1$$.
Reviewer: B.Opic (Praha)

### MSC:

 26D10 Inequalities involving derivatives and differential and integral operators
Full Text: