Nonlinear elliptic equations of order 2m and subdifferentials |
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Authors: | M F Bidaut-Veron |
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Institution: | 1. Département de Mathématiques, Faculté des Sciences, Parc de Grandmont, Tours, France
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Abstract: | LetA be an operator of the calculus of variations of order 2m onW m,p (Ω) andj a normal convex integrand. Forf ∈L p (Ω), the equation $$\mathcal{A}u + \partial j(x,u) \ni f, in \Omega , u - \phi \in W_0^{m,p} (\Omega ),$$ may have no strong solutions whenm>1, even ifj is independent ofx and φ=0. However, we obtain existence results whenj is everywhere finite and $$\int_\Omega {j(x,\phi ) dx< + \infty ,} $$ by the study of the subdifferential of the function $$\upsilon \mapsto \int_\Omega {j(x,\upsilon + \phi ) dx on W_0^{m,p} (\Omega ).} $$ |
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