# مقاله انگلیسی رایگان در مورد اصل فوق العاده بر راه حل ویسکوزیته معادلات لاپلاس بی نهایت – الزویر ۲۰۱۸

 مشخصات مقاله انتشار مقاله سال ۲۰۱۸ تعداد صفحات مقاله انگلیسی ۹ صفحه هزینه دانلود مقاله انگلیسی رایگان میباشد. منتشر شده در نشریه الزویر نوع مقاله ISI عنوان انگلیسی مقاله Superposition principle on the viscosity solutions of infinity Laplace equations ترجمه عنوان مقاله اصل فوق العاده بر راه حل های ویسکوزیته معادلات لاپلاس بی نهایت فرمت مقاله انگلیسی PDF رشته های مرتبط مکانیک، ریاضی گرایش های مرتبط مکانیک سیالات مجله آنالیز غیر خطی – Nonlinear Analysis دانشگاه School of Mathematics and Statistics – Xi’an Jiaotong University – China کلمات کلیدی اصل فوق العاده، معادله لاپلاس بی نهایت، محلول ویسکوزیته کلمات کلیدی انگلیسی Superposition principle, Infinity Laplace equation, Viscosity solution کد محصول E7992 وضعیت ترجمه مقاله ترجمه آماده این مقاله موجود نمیباشد. میتوانید از طریق دکمه پایین سفارش دهید. دانلود رایگان مقاله دانلود رایگان مقاله انگلیسی سفارش ترجمه این مقاله سفارش ترجمه این مقاله

 بخشی از متن مقاله: ۱٫ Introduction The infinity Laplace equation △∞u(x) := ∑ ۱≤i,j≤n uxi uxj uxixj = 0 was introduced by G. Aronsson  in the 1960s. R. Jensen  proved the equivalence of the infinity Laplace equation and the absolutely minimizing Lipschitz extension problem. He also proved the existence and uniqueness of the viscosity solution to the Dirichlet problem: △∞u = 0 in Ω, u = g on ∂Ω for any bounded domain Ω ⊂ R n and g ∈ C(∂Ω). Crandall–Evans–Gariepy  introduced the property of comparison with cones and proved that it is a characteristic property of infinity harmonic functions. The interior regularity for infinity harmonic functions was achieved by Evans, Savin and Smart in [4,14] and . The boundary regularity was studied by Wang–Yu , Hong [6,8] and Hong-Liu . The inhomogeneous infinity Laplace equation: △∞u = f in Ω (۱) was introduced by Lu-Wang . Lindgren  proved that the blow-ups are linear if f ∈ C(Ω)∩L∞(Ω) and u is everywhere differentiable if f ∈ C 1 (Ω) ∩ L∞(Ω). Hong  proved the boundary differentiability of u at a differentiable boundary point and Feng–Hong  studied the slope estimate and boundary differentiability of u on the convex domains. In , Lindgren constructed an extension u˜(x1, . . . , xn+2) = u(x1, . . . , xn) + 5xn+1 + C|xn+2| 4 3 and used the conclusion that if △∞u = f in R n in the viscosity sense then △∞u˜ = f + 2 6 3 4 C in R n+2 in the viscosity sense without a proof. Both of the papers  and  used the same extension and conclusion. The purpose of the extension is to make the slope function strictly positive and the inhomogeneous term bounded away from 0. The conclusion seems obvious but we will see it is not so. In the book (Page 58), Lindqvist also used the similar extension and conclusion. The author gave a very short proof of the conclusion in the footnote, but we do not think the proof is strict enough. The last sentence of the proof says “The desired inequality follows”, but we cannot see why the inequality follows from the proceeding deduction. The argument does not involve an analysis on the second order derivatives, the counterexample in this paper indicates that one should not prove the conclusion without going deep into the analysis on the second order derivatives. In this note, we will give a strict proof of the above mentioned conclusion and provide a counterexample to show that the things are not that simple. We begin by recalling the definition of viscosity solution.