Sectorial Forms and m-Sectorial Operators
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Chapter 11 is concerned with nonsymmetric forms. First, the Lax–Milgram lemma for bounded coercive forms is obtained. The main results of this chapter are two form representation theorems, one for bounded coercive forms on densely and continuously embedded Hilbert spaces and another one for densely defined closed sectorial forms. The latter gives a one-to-one correspondence between densely defined closed sectorial forms and m-sectorial operators. Finally, this form representation theorem is applied to second-order elliptic differential operators.
KeywordsFormal Sector Second-order Elliptic Differential Operator Nonsymmetric Form Continuous Embedding Hilbert Space Isomorphism