Nečas–Lions lemma revisited: An <i>L</i>^<i>p</i>‐version of the generalized Korn inequality for incompatible tensor fields

Abstract

For 1 &lt; p &lt; ∞ , we prove an L p ‐version of the generalized Korn inequality for incompatible tensor fields P in . More precisely, let be a bounded Lipschitz domain. Then there exists a constant c = c ( p , Ω) &gt; 0 such that holds for all tensor fields , that is, for all with vanishing tangential trace on ∂ Ω where ν denotes the outward unit normal vector field to ∂ Ω. For compatible , this recovers an L p ‐version of the classical Korn's first inequality and for skew‐symmetric an L p ‐version of the Poincaré inequality.