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A PRIORI ESTIMATES TO THE MAXIMUM MODULUS OF GENERALIZED SOLUTIONS OF A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS WITH ANISOTROPIC GROWTH CONDITIONS 被引量:1
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作者 梁廷 王向东 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第11期1025-1034,共10页
In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.
关键词 quasilinear elliptic equation. nonstandard growth condition.anisotropic sobolev space. generalized solution. maximum mod-ulus. a priori estimate
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Hölder,Sobolev,weak-type and BMO estimates in mixed-norm with weights for parabolic equations
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作者 Pablo Raúl Stinga José L.Torrea 《Science China Mathematics》 SCIE CSCD 2021年第1期129-154,共26页
We prove weighted mixed-norm Lqt(W2,px)and Lqt(C2,αx)estimates for 1<p,q<∞and 0<α<1,weighted mixed weak-type estimates for q=1,L∞t(Lpx)−BMOt(W2,px)and L∞t(Cαx)−BMOt(C2,xx),and a.e.pointwise formulas ... We prove weighted mixed-norm Lqt(W2,px)and Lqt(C2,αx)estimates for 1<p,q<∞and 0<α<1,weighted mixed weak-type estimates for q=1,L∞t(Lpx)−BMOt(W2,px)and L∞t(Cαx)−BMOt(C2,xx),and a.e.pointwise formulas for derivatives,for the solutions u=u(t,x)to parabolic equations of the form∂tu−aij(t)∂iju+u=f,t∈,x∈n and for the Cauchy problem{∂tv−aij(t)∂ijv+v=fv(0,x)forfort>0,x∈Rn.x∈Rn,The coefficients a(t)=(aij(t))are just bounded,measurable,symmetric and uniformly elliptic.Furthermore,we show strong,weak type and BMO-Sobolev estimates with parabolic Muckenhoupt weights.It is quite remarkable that most of our results are new even for the classical heat equation∂tu−Δu+u=f. 展开更多
关键词 Calderón-Zygmund parabolic singular integrals weak type and BMO estimates representation formulas parabolic equations mixed-norm sobolev and Schauder estimates
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