On generalized Newton’s aerodynamic problem
نویسندگان
چکیده
We consider the generalized Newton’s least resistance problem for convex bodies: minimize functional ? ? ( 1 + stretchy="false">| mathvariant="normal">?<!-- ? <mml:mi>u x , y stretchy="false">) 2 ?<!-- ? <mml:mi>d \iint _\Omega (1 + |\nabla u(x,y)|^2)^{-1} dx\, dy in class of concave functions alttext="u colon right-arrow left-bracket 0 M right-bracket"> :<!-- : stretchy="false">?<!-- ? stretchy="false">[ 0 M stretchy="false">] encoding="application/x-tex">u\colon \Omega \to [0,M] , where domain alttext="normal subset-of double-struck R squared"> ?<!-- ? mathvariant="double-struck">R encoding="application/x-tex">\Omega \subset \mathbb {R}^2 is and bounded alttext="upper greater-than 0"> > encoding="application/x-tex">M > 0 . It has been known (see G. Buttazzo, V. Ferone, B. Kawohl [Math. Nachr. 173 (1995), pp. 71–89]) that if alttext="u"> encoding="application/x-tex">u solves problem, then alttext="StartAbsoluteValue greater-than-or-equal-to 1"> ?<!-- ? encoding="application/x-tex">|\nabla u(x,y)| \ge 1 at all regular points alttext="left-parenthesis right-parenthesis"> encoding="application/x-tex">(x,y) such M"> encoding="application/x-tex">u(x,y) M prove level set L equals StartSet EndSet"> L = fence="false" stretchy="false">{ stretchy="false">} encoding="application/x-tex">L = \{ (x,y)\colon u(x,y) \} nonempty interior, almost its boundary overbar element-of partial-differential L"> stretchy="false">¯<!-- ¯ </mml:mover> ?<!-- ? mathvariant="normal">?<!-- ? encoding="application/x-tex">(\bar {x}, \bar {y}) \in \partial L one alttext="limit StartLayout 1st Row 2nd EndLayout movablelimits="true" form="prefix">lim encoding="application/x-tex">\lim _{\substack {(x,y)\to (\bar {x},\bar {y})\\u(x,y)>M}}|\nabla As a by-product, we obtain result concerning local properties surfaces near ridge points.
منابع مشابه
On Vector Equilibrium Problem with Generalized Pseudomonotonicity
In this paper, first a short history of the notion of equilibrium problem in Economics and Nash$acute{'}$ game theory is stated. Also the relationship between equilibrium problem among important mathematical problems like optimization problem, nonlinear programming, variational inequality problem, fixed point problem and complementarity problem is given. The concept of generalized pseudomonoton...
متن کامل"Gridifying" Aerodynamic Design Problem Using GridRPC
This paper presents a “gridifying” process for aerodynamic wing design as a case study of complex engineering design problems. In order to assist engineers and scientists to solve the problems on the Grid environment effectively, we developed an API based on GridRPC, a Remote Procedure Call standard interface for Grid-enabled applications. In this work, we also provide mechanisms to reduce comm...
متن کاملOn generalized middle-level problem
Let Gn be the subgraph of the hypercube Qn induced by levels between k and n − k, where n ≥ 2k + 1 is odd. The well-known middle level conjecture asserts that G2k+1 is Hamiltonian for all k ≥ 1. We study this problem in Gn for fixed k. It is known that Gn and G 1 n are Hamiltonian for all odd n ≥ 3. In this paper we prove that also Gn is Hamiltonian for all odd n ≥ 5, and we conjecture that Gn ...
متن کاملGeneralized Jacobian and Discrete Logarithm Problem on Elliptic Curves
Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the Moscow Mathematical Society
سال: 2022
ISSN: ['0077-1554', '1547-738X']
DOI: https://doi.org/10.1090/mosc/318