Corrigendum to “Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems”

Abstract EN

In the article titled “Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems” [1], there was an error in Theorem 8.

The operator L:X⊇D(L)→X∗ is assumed to be linear, closed, densely defined, and monotone.

However, it is required to replace this assumption on L by the condition that L:X⊇D(L)→X∗ is linear maximal monotone.

It is known due to Brèzis (cf.

Zeidler [2, Theorem 32.

L, p.897]) that every linear maximal monotone operator is densely defined and closed.

However, the converse is not generally true unless L∗ is monotone.

In addition to conditions on S in Theorem 8 in [1], monotonicity assumption on S (with S(0)=0) is required.

The condition Lx+Sx,x≥-dx2 for all x∈D(L) is not required as it is automatically satisfied with d=0 because of monotonicity of L and S with (L+S)(0)=0.

As a result, Theorem 8 in [1] is restated and replaced by Theorem 1 as follows.