论文标题
完全非线性椭圆方程的分数Sobolev规律性
Fractional Sobolev regularity for fully nonlinear elliptic equations
论文作者
论文摘要
在存在无界源项的情况下，我们证明了完全非线性的椭圆形方程的高阶分数Sobolev规则性。更准确地说，我们显示了一个通用数量的存在$ 0 <\ varepsilon <1 $，仅取决于椭圆性常数和尺寸，因此，如果$ u $是$ f（d^2u）= f（x）= f（x）\ in L^p $的粘度解决方案，则$ u \ in $ u \ in w^{1+\ v varepsilon，pod \ varepsilon，popectiate popectiate popectiation pov^pov^pov^pover。我们的策略提出了完全非线性扩散过程的一种分数特征，因为我们实际上表明的是，对于通用常数$ \ frac {1} {2} {2} {2}<θ<θ<θ<1 $。我们认为我们的技术是灵活的，并且可以适应各种模型和环境。
We prove higher-order fractional Sobolev regularity for fully nonlinear, uniformly elliptic equations in the presence of unbounded source terms. More precisely, we show the existence of a universal number $0< \varepsilon <1$, depending only on ellipticity constants and dimension, such that if $u$ is a viscosity solution of $F(D^2u) = f(x) \in L^p$, then $u\in W^{1+\varepsilon,p}$, with appropriate estimates. Our strategy suggests a sort of fractional feature of fully nonlinear diffusion processes, as what we actually show is that $F(D^2u) \in L^p \implies (-Δ)^θu \in L^p$, for a universal constant $\frac{1}{2} < θ<1$. We believe our techniques are flexible and can be adapted to various models and contexts.
