Archive for Rational Mechanics and Analysis
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Stability in the large of systems of two equations
Archive for Rational Mechanics and Analysis - Tập 7 Số 1 - Trang 119-134 - 1961
Linear Potentials in Nonlinear Potential Theory
Archive for Rational Mechanics and Analysis - Tập 207 Số 1 - Trang 215-246 - 2013
Conservation laws for dynamical systems in Poincaré-Četaev variables
Archive for Rational Mechanics and Analysis - Tập 64 - Trang 327-337 - 1977
On Diffusive 2D Fokker–Planck–Navier–Stokes Systems
Archive for Rational Mechanics and Analysis - Tập 235 Số 3 - Trang 1531-1588 - 2020
On steady three-dimensional motions
Archive for Rational Mechanics and Analysis - Tập 35 - Trang 122-168 - 1969
The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations
Archive for Rational Mechanics and Analysis - 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
Archive for Rational Mechanics and Analysis - Tập 128 Số 4 - Trang 381-399 - 1994
On complete minimal surfaces
Archive for Rational Mechanics and Analysis - Tập 13 Số 1 - Trang 392-404 - 1963
Γ -Entropy Cost for Scalar Conservation Laws
Archive for Rational Mechanics and Analysis - 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.
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