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On solvability of quasilinear elliptic equations in spaces of multipliers. (English) Zbl 0701.35041
Theorems are proved on the solvability of mixed boundary value problems for quasilinear second order elliptic equations and systems in multiplier spaces. Bounded generalized solutions of these equations and systems expressed in divergence form belong to the space MW p 1 (Ω) of multipliers in W p 1 (Ω) under specified conditions. Solutions of a nondivergent equation in the space MS 2 2 (Ω) are treated similarly.
Reviewer: P.A.McCoy
MSC:
35D05Existence of generalized solutions of PDE (MSC2000)
35J25Second order elliptic equations, boundary value problems