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Seminar on nonlinear problems of partial differential equations and mathematical physics
March 26, 2024 18:00, Moscow
 


ON THE STABILITY OF THE FRIEDRICHS INEQUALITY

V. Bobkov

Institute of Mathematics with Computing Centre, Ufa Federal Research Centre, Russian Academy of Sciences, Ufa

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Abstract: We will discuss improvements to the classical Friedrichs inequality, which describes the continuity of the embedding of the Sobolev space $W_0^{1,p}(\Omega)$ into the Lebesgue space $L^q(\Omega)$, in a bounded domain $\Omega$. Namely, in [Bobkov, Kolonitskii, 2023], we obtained several independent versions of the improved Friedrichs inequality. One of them is based on the analysis of quadratic forms associated with the linearization of the p-Laplace operator. Another improvement is based on the stability of the so-called principle of hidden convexity. In both versions, the property of the new improving term is to describe the measure of the distance between a given function and the space of minimizers of the classical Friedrichs inequality. The obtained results are applied to study a nonlinear Fredholm alternative, in particular, to prove the existence of solutions in the resonant case. The talk is based on the work [Bobkov, Kolonitskii, 2023].

Website: https://teams.microsoft.com/l/meetup-join/19%3ameeting_YzMyMjgxMjktYTY5ZC00M2Y4LWIzYTgtNDVjNTMxZTM1Njhh%40thread.v2/0?context=%7b%22Tid%22%3a%222ae95c20-c675-4c48-88d3-f276b762bf52%22%2c%22Oid%22%3a%2266c4b047-af30-41c8-9097-2039bac83cbc%22%7d
 
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