Abstract
Let G be a bounded open subset of Rn and let B be a Dirichlet bilinear form with bounded coefficients defined in G. If the generalized version of Garding's inequality in Lp holds for all u of the Sobolev space W0m,p(G), then we prove under additional assumptions that the form is uniformly elliptic in G and that for n=2 a root condition is satisfied. Further, we study the equivalence of some definitions of “properly elliptic”.
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