On the regularity of the lp minkowski problem

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August undefined, 2024

Web7 de fev. de 2024 · In the present paper, we first introduce the concepts of the Lp n -dimensional Logarithmic-Capacity measure and Lp mixed n -dimensional Logarithmic-Capacity and then prove some geometric properties of Lp n -dimensional Logarithmic-Capacity measure and a Lp Minkowksi inequality for the n -dimensional Logarithmic … Web13 de jul. de 2024 · In this paper, we consider the $L_p$ dual Minkowski problem by geometric variational method. Using anisotropic Gauss–Kronecker curvature flows, we establish the existence of smooth solutions of the $L_p$ dual Minkowski problem when $pq\ge 0$ and the given data is even. If $f\equiv 1$, we show under some restrictions on …

The Lp Minkowski problem for q-capacity - Cambridge Core

WebOn the regularity of the Lp Minkowski problem - CORE Reader 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 … first united methodist hershey

On the regularity of the LpLp Minkowski problem Request PDF

Web29 de jun. de 2024 · In this paper, we prove the uniqueness of the Lp Minkowski problem for q -torsional rigidity with p > 1 and q > 1 in smooth case. Meanwhile, the Lp Brunn-Minkowski inequality and the Lp Hadamard variational formula for q -torsional rigidity are established. Download to read the full article text References Aleksandrov A D. WebON THE Lp-MINKOWSKI PROBLEM ERWIN LUTWAK, DEANE YANG, AND GAOYONG ZHANG ABSTRACT. A volume-normalized formulation of the Lp-Minkowski problem is … WebMinkowski 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 equation theory, Guan and Lin [17] and Chou and Wang [11] focused on the existence and regularity of the Lp Minkowski problem. A solution for p >n +1was camp humphreys sato travel office

$Smooth solutions to the $L_p$ dual Minkowski problem$

Invariant polytopes of linear operators with applications to regularity …

Web1 de jan. de 1995 · PDF On Jan 1, 1995, Erwin Lutwak and others published On the regularity of solutions to a generalization of the Minkowski problem Find, read and … Web1 de jan. de 2006 · Erwin Lutwak, Deane Yang, Gaoyong Zhang, Optimal Sobolev norms and the L p Minkowski problem, International Mathematics Research Notices, Volume 2006, 2006, 62987, ... The Lp-Busemann-Petty centroid inequality, ... On the regularity of solutions to a generalization of the Minkowski problem, ... camp humphreys self helpWebThe Minkowski Problem concerns the existence, uniqueness, and regularity of closed convex hypersurfaces whose Gauss curvature (as a function of the outer normals) is … first united methodist hiawatha ks

"WebIn this paper, we pose two kinds of Minkowski problems involving the p-Laplacian operator. The Hadamard variational formulas for some p-Laplacian functionals are … " - On the regularity of the lp minkowski problem

On the regularity of the lp minkowski problem

WebTheLp-Minkowski problem was ﬂrst formulated and studied in Lutwak[L]. He showed that any even ﬂnite Borel measure is ap-area measure for a unique centrally symmetric convex body. The regularity of the convex body (whenf is regular) was later established in Lutwak-Oliker[LO]. We observe that not every ﬂnite Borel measure is ap-area function. Web1 de jan. de 2024 · In this paper, we study the $ L_p $ dual Minkowski problem, an extension of the dual Minkowski problem. We deal with some cases in which there is no uniform estimate for the Gauss curvature...

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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 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.

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 … 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 …

Web5 de jun. de 2012 · Cone-volume measure, Minkowski problem, Lp-Minkowski problem, log- Minkowski problem. The research of the first author was supported, in part, by EU FP7 IEF grant GEOSUMSET ... Schneider [55] for references). Landmark contributions to establishing regularity for the Minkowski problem are due to (among others) Lewy … WebLp 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

WebThis paper concerns the continuity of the solution to the even Lp Minkowski problem in the plane. When 0 < p < 1, ... S.-Y. Cheng and S.-T. Yau, On the regularity of the solution of the n-dimensional Minkowski problem, Comm. Pure Appl. Math. 29 (1976) 495–561.

WebOn the regularity of the solution of the n-dimensional Minkowski problem. Shiu-Yuen Cheng, Princeton University. Search for more papers by this author. Shing-Tung Yau, … camp humphreys school lunchWeb22 de fev. de 2024 · Precipitation images play an important role in meteorological forecasting and flood forecasting, but how to characterize precipitation images and conduct rainfall similarity analysis is challenging and meaningful work. This paper proposes a rainfall similarity research method based on deep learning by using precipitation images. The … camp humphreys second hand flea marketWebLp-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 ... first united methodist hot springsWebProceedings of the Royal Society of Edinburgh , 151, 1247–1277, 2024 DOI:10.1017/prm.2024.57 The Lp Minkowski problem for q-capacity Zhengmao Chen LCSM (Ministry of ... camp humphreys safety officeWeb10 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 … first united methodist garlandWebThe 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 … camp humphreys sentry mallWeb15 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 … camp humphreys sato office