Selected results and open problems on Hardy-Rellich and Poincare-Friedrische inequalities

We describe 15 open problems

Conformally invariant integral inequalities

We consider hyperbolic isoperimetric inequality and its connections with Euclidean maximum moduli of hyperbolic type plane domains

Selected results and open problems on Hardy-Rellich type inequalities

We describe some open problems connected with our results on Hardy-Rellich type inequalities in space and plane domains

Criteria of positivity of constants in Hardy_Rellich type inequalities

We present main criteria of positivity of constants in Hardy_Rellich type inequalities

Generalizations of Rellich and Birman integral inequaliti

We present our main results connected with Rellich and Birman integral inequalities

Power moments of a domain about its boundary and their applications

We present new results on several estimates for generalized St-Venant functional

Conformally invariant integral inequalities

We present a survey of main known results including author's results

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Criteria of positivity of constants in Hardy-Rellich type inequalities

Geometric problems connected with Hardy-Rellich type inequalities

Estimates of the torsional rigidity and the principal frequency

We investigate criteria of existence of finite constants for a family of inequalities that generalize the Poincar\'{e} -- Friedrichs integral inequality and inequalities for the torsional rigidity.

Integral inequalities of Hardy, their direct generalizations and related inequalities

We present generalizations of Hardy-Rellich_Birman inequalities

Bilateral estimates of functionals of Mathematical Physics

New results on functionals of Mathematical Physics concerning domains with uniformly perfect boundaries.

Strong Hardy type inequalities on domains , lambda close to convex

In Euclidean space we consider domains close to convex in a certain sense. On such domains we establish new Hardy type inequalities with sharp constants.

Hardy type inequalities jn weakly convex domains

We determine sharp constants for two Hardy type inequalities

Some open problems on Hardy-Rellich type inequalities

We presented 7 open problems and related results

Hardy type inequalities

We present convergence theorems for the distance functions and their applications to prove new strong Hardy type inequalities

Criteria of existence of finite constants in basic integral inequalities

we present several criteria of positivity of the first eigenvalue of the Dirichlet problem for the Laplace equation on domains of the Euclidean space and their analogs in inequalities for the torsion rigidity and its generalisations.

Theorem on covergence of gradients of the distance fuctions

We investigate some new properties of the distance functions and applications to the integral variotional inequalities

Hardy and Rellich type conformally invariant inequalities

For test functions we study conformally integral inequalities on domains of the Euclidean space of dimension n using the Loewner-Nirenberg hyperbolic metric.

Hyperbolic domain characteristics and their applications

We examine 4 domain characteristics and their applications to Hardy and Rellich type inequalities

Hardy and Rellich type inequalities

We give a des­cription of this topic during last two years

Some Hardy-type inequalities

Some recent results of the authors are presented

Conformally invariant integral inequalities and their generalizations

For smoorh test functions defined on domains of the Euclidean space we construct and investigate conformally invariant inequalities related to to the n-dimensional Hardy-type inequalities.

Conformally invariant integral inequalities ans their applications

We introduce and investigate several integral conformally invariant inequalities

Hardy and Rellich type inequalities on domains or Euclidean space

We present a selected results of the author durinf last 3 years on two topics. Namely, on inequalities in domains with uniformly perfect boundaries and applications of spaces domains, lambda-close-to-convex.

Generalizations of Rellich inequality with weights

We define special functionals as sharp constants in integral inequalities/ We obtain analogs and generalizations of the Rellich result.

Integral inequalities for polyharmonic operators on plane domains

We investigate geometric functionals defined as sharp constants in Rellich type inequalities for polyharmonic operators.

Geometric des­cription of domains with optimal Hardy constants

We present new results on Hardy type inequalities on domains satisfying the exterior sphere condition

Hardy type inequalities on hyperbolic domains

We describe solutions of several problems on conformally invariant integral inequalities

Hardy type Inequalities

We present our main results about Hardy inequalities in plane and space domains including inequalities for domains with uniformly perfect boundary and geometrical des­cription of non-convex domains with best possible Hardy's constants

Geometrical problems in Hardy type inequalities

We describe families of non-convex domains having maximum possible Hardy constants

Hardy type inequalities

We present neq results on Hardy type inequalities on domains of the Euclidean space.

Hardy type inequalities in multidimensional domains with estimates of constants

We consider Hardy type inequalities in multidimensional domains with estimates of constants

Hardy type inequalities with application to isoperimetric problems

We describe several new results on Hardy type inequalities with application to isoperimetric problems of Mathematical Physics.

Hardy type inequalities with explicit estimates of constants

We presented our results on the Hardy type inequalities with explicit estimates of constants

Hardy type inequalities

New results on Hardy type inequalities