Agnieszka Kałamajska

On a variant of the maximum principle involving radial

We obtain the variant of maximum principle for radial solutions of

p

p

-Laplacian with applications to nonlinear eigenvalue problems and nonexistence results

-harmonic equation

Logarithmic Version of Interpolation Inequalities for Derivatives

-a\Delta_p(w)=\phi(w)

On solutions to the heat equation with the initial condition in the Orlicz—Slobodetskii space

. As a consequence of this result we prove monotonicity of constant sign solutions, analyze the support of the solutions and study their oscillations. The results are applied to various type nonlinear eigenvalue problems and nonexistence theorems.

Weak Lower Semicontinuity by Means of Anisotropic Parametrized Measures

A version of interpolation inequalities for derivatives in logarithmic Orlicz spaces is obtained where the first gradient of is estimated in terms of and its second gradient. One of the Orlicz functions considered is supposed to be . The motivation, examples and applications are discussed.

On Certain New Method to Construct Weighted Hardy-Type Inequalities and Its Application to the Sharp Hardy-Poincaré Inequalities

We study the boundary-value problem ~t = x~ u(x;t), ~ u(x; 0) = u(x), where x2 ;t2 (0;T ), R n 1 is a bounded Lipschitz boundary domain, u belongs to certain Orlicz-Slobodetskii space Y R;R (). Under certain assumptions on the Orlicz function R, we prove that the solution u belongs to Orlicz-Sobolev space W 1;R ( (0;T )).

Oscillation and concentration effects described by Young measures which control discontinuous functions

It is well known that besides oscillations, sequences bounded only in L1 can also develop concentrations, and if the latter occurs, we can at most hope for weak∗ convergence in the sense of measures. Here we derive a new tool to handle mutual interferences of an oscillating and concentrating sequence with another weakly converging sequence. We introduce a couple of explicit examples showing a variety of possible kinds of behavior and outline some applications in Sobolev spaces.

On the completeness of eigenelements of periodic elliptic operators in Besicovitch space B2(Rn)

We apply the recent method of Drabek and the authors in order to construct the Hardy–Poincare–type inequalities