Results 111 to 120 of about 654,419 (234)

Log-Minkowski inequalities for the Lp $L_{p}$-mixed quermassintegrals

Journal of Inequalities and Applications, 2019
Böröczky et al. proposed the log-Minkowski problem and established the plane log-Minkowski inequality for origin-symmetric convex bodies. Recently, Stancu proved the log-Minkowski inequality for mixed volumes; Wang, Xu, and Zhou gave the Lp $L_{p ...
Chao Li, Weidong Wang
doaj   +1 more source

Sobolev and isoperimetric inequalities with monomial weights [PDF]

, 2015
We consider the monomial weight $|x_1|^{A_1}...|x_n|^{A_n}$ in $\mathbb R^n$, where $A_i\geq0$ is a real number for each $i=1,...,n$, and establish Sobolev, isoperimetric, Morrey, and Trudinger inequalities involving this weight. They are the analogue of
Cabre, Xavier, Ros-Oton, Xavier
core  

Decorated phases in triblock copolymers: Zeroth‐ and first‐order analysis

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract We study a two‐dimensional inhibitory ternary system characterized by a free energy functional that combines an interface short‐range interaction energy promoting microdomain growth with a Coulomb‐type long‐range interaction energy that prevents microdomains from unlimited spreading.
Stanley Alama, Lia Bronsard, Xinyang Lu, Chong Wang   +3 more
wiley   +1 more source

Convex dynamics in Hele-Shaw cells

International Journal of Mathematics and Mathematical Sciences, 2002
We study geometric properties of a contracting bubble driven by a homogeneous source at infinity and surface tension. The properties that are preserved during the time evolution are under consideration.
Dmitri Prokhorov, Alexander Vasil'ev
doaj   +1 more source

Transportation-information inequalities for Markov processes (II) : relations with other functional inequalities [PDF]

, 2009
We continue our investigation on the transportation-information inequalities $W_pI$ for a symmetric markov process, introduced and studied in \cite{GLWY}.
Guillin, Arnaud, Leonard, Christian, Wang, Feng-Yu, Wu, Liming   +3 more
core   +4 more sources

Mean‐field behaviour of the random connection model on hyperbolic space

Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.
Abstract We study the random connection model on hyperbolic space Hd${\mathbb {H}^d}$ in dimension d=2,3$d=2,3$. Vertices of the spatial random graph are given as a Poisson point process with intensity λ>0$\lambda >0$. Upon variation of λ$\lambda$, there is a percolation phase transition: there exists a critical value λc>0$\lambda _c>0$ such that for λ<
Matthew Dickson, Markus Heydenreich
wiley   +1 more source

Equivalence of Some Affine Isoperimetric Inequalities

Journal of Inequalities and Applications, 2009
We establish the equivalence of some affine isoperimetric inequalities which include the -Petty projection inequality, the -Busemann-Petty centroid inequality, the "dual" -Petty projection inequality, and the "dual" -Busemann-Petty inequality.
Yu Wuyang
doaj  

A note on Laplacian bounds, deformation properties, and isoperimetric sets in metric measure spaces

Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.
Abstract In the setting of length PI spaces satisfying a suitable deformation property, it is known that each isoperimetric set has an open representative. In this paper, we construct an example of a length PI space (without the deformation property) where an isoperimetric set does not have any representative whose topological interior is nonempty ...
Enrico Pasqualetto, Tapio Rajala
wiley   +1 more source

Orlicz-Aleksandrov-Fenchel Inequality for Orlicz Multiple Mixed Volumes

Journal of Function Spaces, 2018
Our main aim is to generalize the classical mixed volume V(K1,…,Kn) and Aleksandrov-Fenchel inequality to the Orlicz space. In the framework of Orlicz-Brunn-Minkowski theory, we introduce a new affine geometric quantity by calculating the Orlicz first ...
Chang-Jian Zhao
doaj   +1 more source

Brezis–Nirenberg type results for the anisotropic p$p$‐Laplacian

Journal of the London Mathematical Society, Volume 112, Issue 4, October 2025.
Abstract In this paper, we consider a quasilinear elliptic and critical problem with Dirichlet boundary conditions in presence of the anisotropic p$p$‐Laplacian. The critical exponent is the usual p★$p^{\star }$ such that the embedding W01,p(Ω)⊂Lp★(Ω)$W^{1,p}_{0}(\Omega) \subset L^{p^{\star }}(\Omega)$ is not compact.
Stefano Biagi, Francesco Esposito, Alberto Roncoroni, Eugenio Vecchi   +3 more
wiley   +1 more source