Abstract
We show the existence of solution in L p spaces for a generalized form of the classical Von Kármán equations where the coefficients of nonlinear terms are variable. We use Campanato's near operators theory.
Acknowledgements
We thank Professor Piero Villaggio for his useful comments and remarks.
Notes
Notes
1. We set: , while are the exterior normal derivatives at the boundary.
2. d Ω is the diameter of Ω, that is d Ω = sup{|X − Y|, X, Y ∈ Ω}, and
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3. We set: .
4. We denote by ℒ2,λ(Ω), 0 < λ < n + 2, the vector space of the functions u ∈ L 2(Ω) such that
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5. H 2,2,λ(Ω) is the space of the functions to which derivatives of second order belong to ℒ2,λ(Ω).