Global $$W^{1,p}$$W1,p estimates for solutions to the linearized Monge–Ampère equations
Global $$W^{1,p}$$W1,p estimates for solutions to the linearized Monge–Ampère equations
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线性蒙日-安培方程解的全局 $$W^{1,p}$$W1,p 估计
DOI：
10.1007/s12220-016-9739-2
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Truyen V. Nguyen
中科院分区：
文献类型：
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作者：
N. Le;Truyen V. Nguyen
本文研究线性化Monge-Ampère方程在非齐次项具有低可积性时解的正则性。对于右端在$$L^q$$Lq中的方程的解，我们建立了对所有$$p<\frac{nq}{n-q}$$p<nqn-q的全局$$W^{1，p}$$W1，p估计，其中$$n/2<q\le n$$n/2<q≤n.这些估计在自然假设的域，Monge-Ampère措施，和边界数据。我们的估计是N的全局$$W^{1，p}$$W1，p估计的仿射不变类似物。完全非线性一致椭圆方程的Winter解。
In this paper, we investigate regularity for solutions to the linearized Monge–Ampère equations when the nonhomogeneous term has low integrability. We establish global $$W^{1,p}$$W1,p estimates for all $$p<\frac{nq}{n-q}$$p<nqn-q for solutions to the equations with right-hand side in $$L^q$$Lq where $$n/2<q\le n$$n/2<q≤n. These estimates hold under natural assumptions on the domain, Monge–Ampère measures, and boundary data. Our estimates are affine invariant analogues of the global $$W^{1,p}$$W1,p estimates of N. Winter for fully nonlinear, uniformly elliptic equations.