Generation type inequalities for closed linear operators related to domains with conical points

Abstract

Let

be a second-order linear differential operator in divergence form. We prove that the operator

, where λ ∈ C and I stands for the identity operator, is closed and injective when Re λ is large enough and the domain of

consists of a special class of weighted Sobolev function spaces related to conical open bounded sets of R ⁿ , n ≥ 1.

Keywords:

• Resolvent estimates
• Weighted Sobolev function spaces
• Conical bounded domains of Rn
• Mathematics Subject Classifications: 35J25
• 35B45
• 46E35
• 47D06

Notes

Present address. Dipartimento di Matematica “F. Enriques' Via Saldini 50, 20133 Milano, Italy. E-mail: [email protected]

Additional information

Notes on contributors

Alberto Favaron *

Present address. Dipartimento di Matematica “F. Enriques' Via Saldini 50, 20133 Milano, Italy. E-mail: [email protected]