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SUMMARY:Korn and Poincaré-Korn inequalities: A different perspective - Gi
 ovanni Di Fratta (Università degli Studi di Napoli Federico II)
DTSTART:20250819T134500Z
DTEND:20250819T143000Z
UID:TALK234727@talks.cam.ac.uk
DESCRIPTION:Korn's inequality and its variants are essential tools in the 
 mathematical analysis of both linear and nonlinear elasticity. They play a
  central role in establishing existence and regularity results for partial
  differential equations involving symmetric gradients. In this talk\, I wi
 ll present a conceptually simple derivation of the first and second Korn i
 nequalities for general exponents $1 < p < \\infty$\, applicable to a wide
  class of domains\, including Lipschitz and extension domains. Our approac
 h bypasses the traditional reliance on singular integral estimates and int
 ricate geometric arguments\, instead relying on the classical and $q$-Ries
 z representation theorems. In the case $p = 2$\, the argument becomes espe
 cially transparent\, requiring only basic Hilbert space methods and Weyl&r
 squo\;s lemma. I will also discuss associated Poincar&eacute\;--Korn inequ
 alities in both bounded and unbounded domains\, which remain valid even in
  the limiting case $p = 1$. These inequalities not only ensure the coerciv
 ity of variational problems in elasticity but also serve as a key prelimin
 ary step in the proof of the first Korn inequality.
LOCATION:Seminar Room 1\, Newton Institute
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