

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

Number of views: 
This page:  75 

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 pLaplace operator. Another improvement is based on the stability of the socalled 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/meetupjoin/19%3ameeting_YzMyMjgxMjktYTY5ZC00M2Y4LWIzYTgtNDVjNTMxZTM1Njhh%40thread.v2/0?context=%7b%22Tid%22%3a%222ae95c20c6754c4888d3f276b762bf52%22%2c%22Oid%22%3a%2266c4b047af3041c890972039bac83cbc%22%7d

