Abstract
The relationship between the classical interior coercive estimate over W2,2(Ω) and a required boundary coercive estimate for solutions to the L2(∂Ω) Neumann problem is discussed. A conditional lemma in which boundary coerciveness implies interior is proved. Hilbert’s theorem that elliptic operators need not be sums of squares of differential operators and therefore cannot, in general, have formally positive integro–differential forms is discussed. An elliptic operator that is a sum of squares yet has no formally positive coercive form is displayed. The existence of coercive forms for elliptic operators far away from sums of squares is questioned.
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Verchota, G.C. (2010). Boundary Coerciveness and the Neumann Problem for 4th Order Linear Partial Differential Operators. In: Laptev, A. (eds) Around the Research of Vladimir Maz'ya II. International Mathematical Series, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1343-2_17
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