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Local regularity for concave homogeneous complex degenerate elliptic equations dominating the Monge–Ampère equation
Annali di Matematica Pura ed Applicata ( IF 1.0 ) Pub Date : 2021-06-21 , DOI: 10.1007/s10231-021-01129-y Soufian Abja , Guillaume Olive
中文翻译:
主导 Monge-Ampère 方程的凹齐次复简并椭圆方程的局部正则性
更新日期:2021-06-21
Annali di Matematica Pura ed Applicata ( IF 1.0 ) Pub Date : 2021-06-21 , DOI: 10.1007/s10231-021-01129-y Soufian Abja , Guillaume Olive
In this paper, we establish a local regularity result for \(W^{2,p}_{{\mathrm {loc}}}\) solutions to complex degenerate nonlinear elliptic equations \(F(D^2_{\mathbb {C}}u)=f\) when they dominate the Monge–Ampère equation. Notably, we apply our result to the so-called k-Monge–Ampère equation.
中文翻译:
主导 Monge-Ampère 方程的凹齐次复简并椭圆方程的局部正则性
在本文中,我们建立了\(W^{2,p}_{{\mathrm {loc}}}\)复杂退化非线性椭圆方程的解的局部正则性结果\(F(D^2_{\mathbb { C}}u)=f\)当它们支配 Monge-Ampère 方程时。值得注意的是,我们将我们的结果应用于所谓的k -Monge-Ampère 方程。