Archive for Rational Mechanics and Analysis
1432-0673
0003-9527
Cơ quản chủ quản: Springer New York , SPRINGER
Lĩnh vực:
Mathematics (miscellaneous)Mechanical EngineeringAnalysis
Phân tích ảnh hưởng
Thông tin về tạp chí
Các bài báo tiêu biểu
The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations
Tập 101 - Trang 1-27 - 1988
We prove that viscosity solutions in W
1,∞ of the second order, fully nonlinear, equation F(D
2
u, Du, u) = 0 are unique when (i) F is degenerate elliptic and decreasing in u or (ii) F is uniformly elliptic and nonincreasing in u. We do not assume that F is convex. The method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions onto viscosity subsolutions and supersolutions, respectively. This method is completely different from that used in Lions [8, 9] for second order problems with F convex in D
2
u and from that used by Crandall & Lions [3] and Crandall, Evans & Lions [2] for fully nonlinear first order problems.
An elementary proof of the polar factorization of vector-valued functions
Tập 128 Số 4 - Trang 381-399 - 1994
Γ -Entropy Cost for Scalar Conservation Laws
Tập 195 - Trang 261-309 - 2008
We are concerned with a control problem related to the vanishing viscosity approximation to scalar conservation laws. We investigate the Γ -convergence of the control cost functional, as the viscosity coefficient tends to zero. A first-order Γ -limit is established, which characterizes the measure-valued solutions to the conservation laws as the zeros of the Γ -limit. A second-order Γ -limit is then investigated, providing a characterization of entropic solutions to conservation laws as the zeros of the Γ -limit.