I. Skrypnik

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math.AP2025

Qualitative properties of solutions to parabolic anisotropic equations: Part I -- Expansion of positivity

Simone Ciani, Eurica Henriques, Mariia Savchenko +1

We prove expansion of positivity and reduction of the oscillation results to the local weak solutions to a doubly nonlinear anisotropic class of parabolic differential equations wi…

math.AP2025

Parabolic De Giorgi classes with doubly nonlinear, nonstandard growth: local boundedness under exact integrability assumptions

Simone Ciani, Eurica Henriques, Mariia O. Savchenko +1

We define a suitable class $PD G$ of functions bearing unbalanced energy estimates, that are embodied by local weak subsolutions to doubly nonlinear, double-phase, Orlicz-…

math.AP2025

On the continuity of solutions to the anisotropic $N$ -Laplacian with $L^{1}$ lower order term

Mariia Savchenko, Igor Skrypnik, Yevgeniia Yevgenieva

We establish the continuity of bounded solutions to the anisotropic elliptic equation $$-\sum\limits_{i=1}^N\Big(|u_{x_i}|^{p_i-2} u_{x_i}\Big)_{x_i}=f(x),\quad x\in Ω,\quad f(x)\i…

Qualitative properties of solutions to parabolic anisotropic equations: Part I -- Expansion of positivity

Parabolic De Giorgi classes with doubly nonlinear, nonstandard growth: local boundedness under exact integrability assumptions

On the continuity of solutions to the anisotropic N-Laplacian with L1 lower order term

On the continuity of solutions to the anisotropic $N$ -Laplacian with $L^{1}$ lower order term