Functional classes of solutions of elliptic equations with non-standard growth conditions
According to the materials of report at the meeting of the Presidium of the NAS of Ukraine, December 26, 2024
DOI:
https://doi.org/10.15407/visn2025.02.074Abstract
The report presents the results of the research on functional classes of solutions of elliptic equations with non-standard growth conditions. These classes of solutions cover new cases of non-uniformly elliptic two-phase equations, degenerate two-phase equations, and equations with variable nonlinearity exponents. It is proved that functions from these classes are continuous and satisfy Harnack inequalities. One of the key innovations is the development of a universal approach to describe elliptic equations with non-standard growth conditions through a precise version of the generalized non-logarithmic continuity condition for the coefficients.
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