Advances in Nonlinear Analysis, 2014 We obtain a new Liouville comparison principle for weak solutions (u,v) of semilinear parabolic second-order partial differential inequalities of the form ut-ℒu-|u|q-1u≥vt-ℒv-|v|q-1v(*)$u_t -{\mathcal {L}}u- |u|^{q-1}u\ge v_t -{\mathcal {L}}v- |v|^{q-1}v\
Kurta Vasilii V.
doaj +1 more source
A Liouville comparison principle for solutions of quasilinear singular parabolic inequalities
Advances in Nonlinear Analysis, 2015 We obtain a Liouville comparison principle for entire weak solutions (u,v) of quasilinear singular parabolic second-order partial differential inequalities of the form ut-A(u)-|u|q-1u≥vt-A(v)-|v|q-1v${ u_t - A(u)-|u|^{q-1}u \ge v_t - A (v)-|v|^{q-1}v ...
Kurta Vasilii V.
doaj +1 more source
Uniqueness and comparison principles for semilinear equations and inequalities in Carnot groups
Advances in Nonlinear Analysis, 2018 Variants of the Kato inequality are proved for distributional solutions of semilinear equations and inequalities on Carnot groups. Various applications to uniqueness, comparison of solutions and Liouville theorems are presented.
D’Ambrosio Lorenzo, Mitidieri Enzo
doaj +1 more source
Penerapan Metode User Centered Design dalam Perancangan Ulang Desain Website MAN 1 Pasuruan [PDF]
, 2022 Dalam membangun citra positif sebagai lembaga pendidikan berbasis islam yang optimis dan mampu bersaing dengan sekolah umum secara kompetitif, MAN 1 Pasuruan mengembangkan sebuah website yang berfungsi sebagai wadah informasi dan media peningkatan citra ...
Cahyani, Rizka Dwi +1 more
core +1 more source
Existence and non-existence of global solutions for semilinear heat equations and inequalities on sub-Riemannian manifolds, and Fujita exponent on unimodular Lie groups [PDF]
, 2018 In this paper we study the global well-posedness of the following Cauchy problem on a sub-Riemannian manifold $M$: \begin{equation*} \begin{cases} u_{t}-\mathfrak{L}_{M} u=f(u), \;x\in M, \;t>0, \\u(0,x)=u_{0}(x), \;x\in M, \end{cases} \end{equation ...
Ruzhansky, M, Yessirkegenov, N
core +2 more sources
Smooth counterexamples to strong unique continuation for a Beltrami system in $\mathbb{C}^2$ [PDF]
, 2011 We construct an example of a smooth map $\mathbb{C}\to\mathbb{C}^2$ which vanishes to infinite order at the origin, and such that the ratio of the norm of the $\bar z$ derivative to the norm of the $z$ derivative also vanishes to infinite order.
Coffman, Adam, Pan, Yifei
core +3 more sources
C^{1,1} regularity for degenerate elliptic obstacle problems
, 2016 The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing,
Daskalopoulos, Panagiota +1 more
core +1 more source
, 2013 We prove existence and uniqueness of stochastic representations for solutions to elliptic and parabolic boundary value and obstacle problems associated with a degenerate Markov diffusion process.
Feehan, Paul M. N., Pop, Camelia
core +1 more source
On a sharp Poincare-type inequality on the 2-sphere and its application in micromagnetics [PDF]
, 2019 The main aim of this note is to prove a sharp Poincar\'e-type inequality for vector-valued functions on $\mathbb{S}^2$, that naturally emerges in the context of micromagnetics of spherical thin films.Comment: 2 ...
Di Fratta, Giovanni +2 more
core +4 more sources
Maximum principles for boundary-degenerate second-order linear elliptic differential operators
, 2013 We prove weak and strong maximum principles, including a Hopf lemma, for smooth subsolutions to equations defined by linear, second-order, partial differential operators whose principal symbols vanish along a portion of the domain boundary.
Feehan, Paul M. N.
core +1 more source