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Volume 10, Issue 1
Regularity Results for Minimizers of Certain Functional Having Nonquadratic Growth with Obstacles

Minchun Hong

J. Part. Diff. Eq., 10 (1997), pp. 65-84.

Published online: 1997-10

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  • 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
  • Keywords

Degenerate variational integral obstacle partial regularity

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@Article{JPDE-10-65, author = {}, title = {Regularity Results for Minimizers of Certain Functional Having Nonquadratic Growth with Obstacles}, journal = {Journal of Partial Differential Equations}, year = {1997}, volume = {10}, number = {1}, pages = {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}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5582.html} }
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
Minchun Hong . (2019). Regularity Results for Minimizers of Certain Functional Having Nonquadratic Growth with Obstacles. Journal of Partial Differential Equations. 10 (1). 65-84. doi:
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