Art

J-GLOBAL ID：202102241693163355   Reference number：21A0255879

Equivalence of Viscosity Solutions between Obstacle and Gradient Constraint Problems

障害物と勾配制約の間の問題に対する粘性解の等価性

Author (1)： Kosugi Takahiro (Tottori University of Environmental Studies)
Material： Funkcialaj Ekvacioj. International Series  (Funkcialaj Ekvacioj)
Volume： 63  Issue： 3  Page： 323-343(J-STAGE)  Publication year： 2020 
JST Material Number： L4931A  ISSN： 0532-8721  Document type： Article
Article type： 原著論文  Country of issue： Japan (JPN)  Language： ENGLISH (EN)

Thesaurus term： *solution (mathematics) ,  gradient ,  *constraint condition (restriction) ,  *partial differential equation ,  obstruction ,  condition ,  degeneracy ,  *elliptic partial differential equation
Semi thesaurus term： Lipschitz condition ,  *constraints ,  *viscosity solution

Author keywords (4)： Bilateral obstacle ,  Gradient constraint ,  Viscosity solution ,  Singular elliptic equation

JST classification (1)： Mathematical physics  (BA03000W)

Reference (24)：

• [1] Attouchi, A., Parviainen, M. and Ruosteenoja, E., C^1,α regularity for the normalized p-Poisson problem, J. Math. Pures Appl., 108 (2017), 553-591.
• [2] Barles, G., A weak Bernstein method for fully nonlinear elliptic equations, Differential Integral Equations, 4 (1991), 241-262.
• [3] Barles, G., Biton, S., Bourgoing, M. and Ley, O., Uniqueness results for quasilinear parabolic equations through viscosity solutions' methods, Calc. Var. Partial Differential Equations, 18 (2003), 159-179.
• [4] Brezis, H. and Sibony, M., Équivalence de deux inéquations variationnelles et applications, Arch. Rational Mech. Anal., 41 (1971), 254-265.
• [5] Crandall, M. G., Ishii, H. and Lions, P.-L., User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., 27 (1992), 1-67.

Terms in the title (5)： 障害物 ,  勾配 ,  制約 ,  粘性解 ,  等価性