A Compact Course on Linear PDEs: 126: Valli, Alberto

The Atmosphere and the Sea in Motion - NYU Courant

Ran(T ) is closed. 3. Coker(T ) is ﬁnite dimensional. If T is Fredholm deﬁne the index of T denoted Ind(T ) to be the number dim(ker(T ))− dim(Coker(T )) First let us show that the closed range condition is redundant. Lemma 16.14. holm alternative applies beyond linear problems to cases where the linearity as-sumption is replaced by conditions of homogeneity.