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Volume 5, Issue 3
The Obstacle Problems for Second Order Fully Nonlinear Elliptic Equations with Neumann Boundary Conditions

Bao Jiguang

J. Part. Diff. Eq.,5(1992),pp.33-45

Published online: 1992-05

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  • Abstract
In this paper we prove the existence theorem of the strong solutions to the obstacle problems for second order fully nonlinear elliptic equations with the Neumann boundary conditions F(x, u, Du, D²u) ≥ 0, x ∈ Ω u ≤ g, x ∈ Ω (u - g)F(x, u, Du, D²u) = 0, x ∈ Ω D_vu = φ(x, u), x ∈ ∂Ω where F(x, z, p, r) satisfies the natural structure conditions and is concave with respect to r, p, and φ(x, z) is nondecreasing in z, and g(x) satisfies the consistency condition.
  • Keywords

Obstacle problems Neumann boundary conditions logarithmic modulus of semicontinuity global second derivative estimates

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COPYRIGHT: © Global Science Press

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@Article{JPDE-5-33, author = {Bao Jiguang}, title = {The Obstacle Problems for Second Order Fully Nonlinear Elliptic Equations with Neumann Boundary Conditions}, journal = {Journal of Partial Differential Equations}, year = {1992}, volume = {5}, number = {3}, pages = {33--45}, abstract = { In this paper we prove the existence theorem of the strong solutions to the obstacle problems for second order fully nonlinear elliptic equations with the Neumann boundary conditions F(x, u, Du, D²u) ≥ 0, x ∈ Ω u ≤ g, x ∈ Ω (u - g)F(x, u, Du, D²u) = 0, x ∈ Ω D_vu = φ(x, u), x ∈ ∂Ω where F(x, z, p, r) satisfies the natural structure conditions and is concave with respect to r, p, and φ(x, z) is nondecreasing in z, and g(x) satisfies the consistency condition.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5743.html} }
TY - JOUR T1 - The Obstacle Problems for Second Order Fully Nonlinear Elliptic Equations with Neumann Boundary Conditions AU - Bao Jiguang JO - Journal of Partial Differential Equations VL - 3 SP - 33 EP - 45 PY - 1992 DA - 1992/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5743.html KW - Obstacle problems KW - Neumann boundary conditions KW - logarithmic modulus of semicontinuity KW - global second derivative estimates AB - In this paper we prove the existence theorem of the strong solutions to the obstacle problems for second order fully nonlinear elliptic equations with the Neumann boundary conditions F(x, u, Du, D²u) ≥ 0, x ∈ Ω u ≤ g, x ∈ Ω (u - g)F(x, u, Du, D²u) = 0, x ∈ Ω D_vu = φ(x, u), x ∈ ∂Ω where F(x, z, p, r) satisfies the natural structure conditions and is concave with respect to r, p, and φ(x, z) is nondecreasing in z, and g(x) satisfies the consistency condition.
Bao Jiguang. (1970). The Obstacle Problems for Second Order Fully Nonlinear Elliptic Equations with Neumann Boundary Conditions. Journal of Partial Differential Equations. 5 (3). 33-45. doi:
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