The second order elliptic differential equations are considered in an exterior domain Ω Rn, n≥2, where p can chang sign. Some new sufficient conditions for the oscillation of solutions of (1.1) and (1.2) are establi...The second order elliptic differential equations are considered in an exterior domain Ω Rn, n≥2, where p can chang sign. Some new sufficient conditions for the oscillation of solutions of (1.1) and (1.2) are established.展开更多
The authors study homogenization of some nonlinear partial differential equations of the form -div (?(hx, h2x,Duh)) =f, where a is periodic in the first two arguments and monotone in the third. In particular the case ...The authors study homogenization of some nonlinear partial differential equations of the form -div (?(hx, h2x,Duh)) =f, where a is periodic in the first two arguments and monotone in the third. In particular the case where a satisfies degenerated structure conditions is studied. It is proved that uh converges weakly in W01,1 (?) to the unique solution of a limit problem as h ? '. Moreover, explicit expressions for the limit problem are obtained.展开更多
In this paper,we mainly discuss a priori bounds of the following degenerate elliptic equation,a^ ij（x）δij u＋b^ i（x）δiu＋f（x,u）=0,in Ω belong to belong toR^n,（＊）where a^ijδiφδjφ=0 on δΩ,andφis the d...In this paper,we mainly discuss a priori bounds of the following degenerate elliptic equation,a^ ij（x）δij u＋b^ i（x）δiu＋f（x,u）=0,in Ω belong to belong toR^n,（＊）where a^ijδiφδjφ=0 on δΩ,andφis the defining function of δΩ.Imposing suitable conditions on the coefficients and f（x,u）,one can get the L^∞-estimates of（＊）via blow up method.展开更多
文摘The second order elliptic differential equations are considered in an exterior domain Ω Rn, n≥2, where p can chang sign. Some new sufficient conditions for the oscillation of solutions of (1.1) and (1.2) are established.
文摘The authors study homogenization of some nonlinear partial differential equations of the form -div (?(hx, h2x,Duh)) =f, where a is periodic in the first two arguments and monotone in the third. In particular the case where a satisfies degenerated structure conditions is studied. It is proved that uh converges weakly in W01,1 (?) to the unique solution of a limit problem as h ? '. Moreover, explicit expressions for the limit problem are obtained.
基金supported by National Natural Science Foundation of China(Grant No.11131005)
文摘In this paper,we mainly discuss a priori bounds of the following degenerate elliptic equation,a^ ij（x）δij u＋b^ i（x）δiu＋f（x,u）=0,in Ω belong to belong toR^n,（＊）where a^ijδiφδjφ=0 on δΩ,andφis the defining function of δΩ.Imposing suitable conditions on the coefficients and f（x,u）,one can get the L^∞-estimates of（＊）via blow up method.
