Year: 1997
Journal of Partial Differential Equations, Vol. 10 (1997), Iss. 1 : pp. 65–84
Abstract
We prove partial regularity for minimizers of degenerate variational integrals ∫_Ω F(x, u, Du)dx with obstacles of either the form (i) μ_f = {u ∈ H^{1,m} (Ω,\mathbb{R}^N)|u^N ≥ f_1(u¹, ... ,u^{N-1}) + f_2(x) a.e.} or (ii) μ_N = {u ∈ H^{1,m}(Ω,\mathbb{R}^N)|u^i(x) ≥ h^i(x), a.e.; i=1, ... ,N} The typical mode of variational integrals is given by ∫_Ω [a^{αβ}(x, u)b_{ij}(x, u)D_αu^i D_βu^i]^{\frac{m}{2}}dx, m ≥ 2
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1997-JPDE-5582
Journal of Partial Differential Equations, Vol. 10 (1997), Iss. 1 : pp. 65–84
Published online: 1997-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Degenerate variational integral