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Robin boundary value problems on arbitrary domains. (English) Zbl 0947.35072
The Robin boundary value problems for quasilinear divergent elliptic equations of the second order on domains with nonsmoothness boundaries are investigated. \(L_p\)-estimates for the weak solutions are obtained. The theory of Sobolev spaces on arbitrary domains developed by Maz’ja was used. These estimates and the Moser iteration technique are basic for the construction of the \(L_p\)-theory for Robin boundary value problems on arbitrary domains. The semigroup theory is applied for the investigation of the uniqueness of the corresponding parabolic problems.

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35D10 Regularity of generalized solutions of PDE (MSC2000)
35B45 A priori estimates in context of PDEs
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