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Article Contents

# Operators of order 2$n$ with interior degeneracy

• * Corresponding author: Rosa Maria Mininni

Dedicated to Gisèle Ruiz Goldstein, outstanding mathematician, with great admiration and friendship on her 60th birthday

• We consider a differential operator of order 2$n$ of the type $A_n u = (-1)^n (a u^{(n)})^{(n)}$, where $a(x)>0$ in $[0, 1]\setminus\{x_0\}$ and $a(x_0) = 0$. We show that, for any $n\in{\mathbb{N}}$, the operator $-A_n$ generates a contractive analytic semigroup of angle $\pi/2$ on $L^2 (0, 1)$. Note that the domain of $A_n$ depends on the type of degeneracy of $a$. Our theorems extend some previous results in [3] where $n = 1$.

Mathematics Subject Classification: Primary: 47D06, 35K65; Secondary: 47B25, 47N20.

 Citation:

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