In this paper we give a survey of selected results and open problems on integral inequalities
of Mathematical Physics connected with the papers of V. Maz'ya, S. Fillippas, A. Tertikas, R …

For test functions supported in a domain of the Euclidean space we consider the Hardy–
Rellich inequality:∫| Δ f| 2 dx≥ C 2∫| f| 2 δ− 4 (x) dx, where C 2= const≥ 0 and δ (x) is the …

arXiv:2408.00013v2 [math.AP] 27 Sep 2024 Page 1 arXiv:2408.00013v2 [math.AP] 27 Sep 2024
FACTORIZATIONS AND POWER WEIGHTED RELLICH AND HARDY–RELLICH-TYPE …

The principal aim of this note is to illustrate how factorizations of singular, even-order partial
differential operators yield an elementary approach to classical inequalities of Hardy-Rellich …

In this paper our primary concern is with the establishment of weighted Hardy inequalities in
Lp (Ω) and Rellich inequalities in L2 (Ω) depending upon the distance to the boundary of …

Mathematische Zeitschrift Page 1 Math. Z. (2007) 255:877–896 DOI 10.1007/s00209-006-0056-5
Mathematische Zeitschrift Best constants for higher-order Rellich inequalities in L p( ) G …

We obtain L_p L p analogues of the classical Rellich inequality in general open subsets Ω Ω
of R^ n R n and similar inequalities involving the p-Laplacian. We also examine the …

In 1987, our book Spectral Theory and Differential Operators was published. It emphasised
the symbiotic relationship, as we saw it, between the theory of compact linear operators …

We give improvements and generalizations of both the classical Hardy inequality and the
geometric Hardy inequality based on the divergence theorem. Especially, our improved …

Hardy and Rellich type inequalities with an additional term are proved for compactly
supported smooth functions on open subsets of the Euclidean space. We obtain one …