Agnieszka Kałamajska

activity

20092026

most citedOn a variant of Gagliardo-Nirenberg inequality deduced from Hardy

5 citations · 16 across the 14 of their papers we have counts for

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10 papers · 1 filter

math.AP2026

Singular semilinear elliptic equations in nondivergence form

Agnieszka Kałamajska, Dalimil Peša, Artur Rutkowski

We study the singular semilinear equation $- P u = \frac{f}{u ^{γ}}$ on a bounded domain $Ω$ with Dirichlet condition $u \equiv 0$ on $\partial Ω$ , where $P$ is a second-order elliptic…

math.AP2023★ 1 cited

Non-linear Gagliardo--Nirenberg inequality involving a second-order elliptic operator in non-divergent form

Agnieszka Kałamajska, Dalimil Peša, Tomáš Roskovec

We obtain the inequalities of the form $\int_{Ω} ∣\nabla u (x) ∣^{2} h (u (x)) d x \leq C \int_{Ω} (∣ P u (x) ∣∣ T_{H} (u (x)) ∣)^{2} h (u (x)) d x + Θ,$ where $Ω…

math.AP2019

On maximum principles for radial solutions to nonlinear elliptic PDE's via Opial-type inequalities

Agnieszka Kałamajska, Anna Kosiorek

We consider degenerated nonlinear PDE of elliptic type: $- div (a (∣ x ∣) ∣\nabla w (x) ∣^{p - 2} \nabla w (x)) + h (∣ x ∣, w (x), ⟨ \nabla w (x), \frac{x}{∣ x ∣} ⟩) = ϕ (w (x)),$ w…

math.AP2018

On one variant of strongly nonlinear Gagliardo-Nirenberg inequality involving Laplace operator with application to nonlinear elliptic problems

Agnieszka Kałamajska, Tomasz Choczewski

We obtain the inequality $\int_{Ω} ∣\nabla u (x) ∣^{p} h (u (x)) d x \leq C (n, p) \int_{Ω} (∣Δ u (x) ∣∣ T_{h, C} (u (x)) ∣)^{p} h (u (x)) d x,$ where $Ω \subset R^{n}$ is a bo…

math.AP2017

Weak lower semicontinuity by means of anisotropic parametrized measures

Agnieszka Kałamajska, Stefan Krömer, Martin Kružík

It is well known that besides oscillations, sequences bounded only in $L^{1}$ can also develop concentrations, and if the latter occurs, we can at most hope for weak $^{*}$ convergence…

math.AP2016

On certain variant of strongly nonlinear interpolation inequality in dimension n

Tomasz Choczewski, Agnieszka Kałamajska

We obtain the inequality $\int_{Ω} ∣\nabla u (x) ∣^{p} h (u (x)) d x \leq C (n, p) \int_{Ω} (∣ \nabla^{(2)} u (x) ∣∣ T_{h, C} (u (x)) ∣)^{p} h (u (x)) d x,$ where $Ω\subseteq {\bf R}…

math.AP2016★ 4 cited

Caccioppoli--type estimates and Hardy--type inequalities derived from degenerated $p$ --harmonic problems

Pavel Drábek, Agnieszka Kałamajska, Iwona Skrzypczak

We obtain Caccioppoli--type estimates for nontrivial and nonnegative solutions to the anticoercive partial differential inequalities of elliptic type involving degenerated $p$ --Lap…

math.AP2012★ 1 cited

Sequential weak continuity of null Lagrangians at the boundary

Agnieszka Kalamajska, Stefan Kroemer, Martin Kruzik

We show weak* in measures on $Ø ˉ$ / weak- $L^{1}$ sequential continuity of $u \mapsto f (x, \nabla u) : W^{1, p} (Ø; R^{m}) \to L^{1} (Ø)$ , where $f (x, \cdot)$ is a null Lagrangian for $x \in Ø$ , i…

math.AP2011

On some nonlinear extensions of the Gagliardo-Nirenberg inequality with applications to nonlinear eigenvalue problems

Agnieszka Kałamajska, Jan Peszek

We derive inequality [\int_{\r} |f^{'}(x)|^ph(f(x))dx \le (\sqrt{p-1})^p\int_{\r}(\sqrt{|f^{"}(x){\cal T}_h(f(x))|})^ph(f(x))dx,] where $f$ belongs locally to Sobolev space $W^{2,1…

math.AP2009★ 5 cited

On a variant of Hardy inequality between weighted Orlicz spaces

Agnieszka Kalamajska, Katarzyna Pietruska-Paluba

Let M be an N-function satisfying the $Δ_{2}$ - condition, let $ω, \vp$ be two other functions, $ω \geq 0$ . We study Hardy-type inequalities \[ \int_{\rp} M(ω(x)|u(x)|) {\rm exp}(-\vp (…