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On the regularity of the lp minkowski problem

Web5 de jun. de 2024 · Lutwak, Yang and Zhang [24] formulated the L p dual Minkowski problem, which concerns the characterization of L p dual curvature measures. In this paper, we solve the existence part of the L p dual Minkowski problem for p > 1 and q > 0, and we also discuss the regularity of the solution. article Next article 52A40 Keywords Web21 de set. de 2024 · The Lp Minkowski problem for q-capacity - Volume 151 Issue 4. Skip to main content Accessibility help ... Regularity and free boundary regularity for the p-Laplace operator in Reifenberg flat and Ahlfors regular …

A flow approach to the planar Lp$L_p$ Minkowski problem

Web1 de dez. de 2003 · Thus the Lp -Minkowski problem concerns the existence of a closed convex hypersurface whose reciprocal Gauss curvature is ghp−1, where h is the support … WebMinkowski solved the problem in the category of polyhedrons. Then A. D. Alexandrov and others solved the problem in general. However, this last solution does not provide any … hideout\u0027s kc https://rmdmhs.com

Continuity of the Solution to the Lp Minkowski Problem in …

Web15 de set. de 2024 · In this paper, it is proved that the weak convergence of the Lp Gaussian surface area measures implies the convergence of the corresponding convex bodies in the Hausdorff metric for p ≥ 1. Moreover, continuity of the solution to the Lp Gaussian Minkowski problem with respect to p is obtained. Download to read the full … WebLp-Minkowski problem is quite different from the path taken in [Lul] in solving the even Lp-Minkowski problem. The solution to the volume-normalized even Lp-Minkowski problem for all p > 1 is needed in [LuYZ2]. A compact convex subset of Euclidean n-space Rn will be called a convex body. Associated with a convex body K is its support function h ... Web10 de mar. de 2024 · The -Minkowski problem with super-critical exponents Qiang Guang, Qi-Rui Li, Xu-Jia Wang The -Minkowski problem deals with the existence of closed … hideout\\u0027s ix

Continuity of the Solution to the Lp Minkowski Problem in …

Category:[PDF] On the _{}-Minkowski problem Semantic Scholar

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On the regularity of the lp minkowski problem

Flow by Gauss curvature to the $ L_p $ dual Minkowski problem

Web21 de set. de 2024 · With the Hadamard variational formula, variational method and Lp Minkowski inequality mentioned above, we prove the existence and uniqueness of the … WebA new approach to theLp-Minkowski problem is presented, which solves the volume-normalized formulation for even data and allp 1. TheMinkowski problemdeals with existence, uniqueness, regularity, and sta- bility of closed convex hypersurfaces whose Gauss curvature (as a function of the outer normals) is preassigned.

On the regularity of the lp minkowski problem

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Webp Brunn-Minkowski theory is the L p Minkowski problem. A solution to the L p Minkowski problem when the data is even was given in [11]. This solution turned out to be a critical ingredient in the recently established L p affine Sobolev inequality [17]. Suppose the real index p is fixed. The L p Minkowski problem for polytopes asks for the WebThe works of Guan and Lin [8] and Chou and Wang [5] focus on existence and regularity for the L p Minkowski problem. Both works make use of the machinery of the theory of …

Web1 de fev. de 2013 · The LpLp Minkowski problem is equivalent to solve the Monge–Ampère equationdet (uij+uδij)=up−1f,on Sn. Since it is degenerate for … Web11 de abr. de 2024 · Publisher preview available. A flow approach to the planar Lp$L_p$ Minkowski problem. April 2024; Mathematische Nachrichten

WebMinkowski problem (1.1), B or oczky-Lutwak-Yang-Zhang [5] obtained the existence of the even logarithmic Minkowski problem provided that the given measure satis ed the …

Web19 de jun. de 2024 · In this paper we study the Lpq -dual Minkowski problem for the case p < 0 < q. We prove for any positive smooth function f on \mathbb {S}^ {1}, there exists an F: ℝ + → ℝ −, such that if F ( q) < p < 0 or 0 < q < − F (− p) then there is a smooth and strictly convex body solving the planar Lpq -dual Minkowski problem.

WebLp-Minkowski problem (q= n). The dual Minkowski problem was first pro-posed by Huang, Lutwak, Yang and Zhang in their recent groundbreaking work [18] and then followed by [4, 15, 17, 29, 46, 47 ... hideout\u0027s kbWeb15 de dez. de 2003 · On the _ {}-Minkowski problem. A volume-normalized formulation of the Lp-Minkowski problem is presented. This formulation has the advantage that a … hideout\\u0027s kwWebA new approach to the Lp-Minkowski problem is presented, which solves the volume-normalized formulation for even data and all p ≥ 1. The Minkowski problem deals with … hideout\\u0027s khWebMinkowski problem for polytopes and applications of the Lp Minkowski problem to sharp affine in-variant Lp Sobolevinequalities [26,27]. From the view of partial differential … hideout\\u0027s kgWeb6 de jun. de 2024 · A regular solution of Minkowski's problem has been given by A.V. Pogorelov in 1971 (see ); he also considered certain questions in geometry and in the … hideout\u0027s khWebLp Minkowski problem for electrostatic p-capacity Du Zou1 Ge Xiong2 1. Department of Mathematics, Wuhan University of Science and Technology, Wuhan, ... Establishing the regularity of the solution to the Minkwoski problem is difficult and has led to a long series of highly influential works, see, e.g., Lewy [42], Nirenberg hideout\\u0027s k1Web1 de jan. de 1995 · In [23], Lutwak proved that the solution to the L p Minkowski problem is unique for > p 1 and ≠ p n if μ is even and positive. In [24], Lutwak and Oliker proved the regularity of the solution... how family influence child development