TY - JOUR
T1 - Regularity Results for Minimizers of Certain Functional Having Nonquadratic Growth with Obstacles
JO - Journal of Partial Differential Equations
VL - 1
SP - 65
EP - 84
PY - 1997
DA - 1997/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5582.html
KW - Degenerate variational integral
KW - obstacle
KW - partial regularity
AB -  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