Tomasz Choczewski

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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.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}…