Results 71 to 80 of about 425 (156)
The Cheeger problem in abstract measure spaces
Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.Abstract We consider nonnegative σ$\sigma$‐finite measure spaces coupled with a proper functional P$P$ that plays the role of a perimeter. We introduce the Cheeger problem in this framework and extend many classical results on the Cheeger constant and on Cheeger sets to this setting, requiring minimal assumptions on the pair measure space perimeter ...
Valentina Franceschi +3 more
wiley +1 more source
ASYMPTOTIC EXPANSION OF THE DENSITY FOR HYPOELLIPTIC ROUGH DIFFERENTIAL EQUATION [PDF]
Nagoya Mathematical Journal, 2019 We study a rough differential equation driven by fractional Brownian motion with Hurst parameter $H$$(1/4<H\leqslant 1/2)$. Under Hörmander’s condition on the coefficient vector fields, the solution has a smooth density for each fixed time. Using Watanabe’s distributional Malliavin calculus, we obtain a short time full asymptotic expansion of the ...
Inahama, Yuzuru, Naganuma, Nobuaki
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Some properties of solutions to weakly hypoelliptic equations [PDF]
, 2012 A linear differential operator L is called weakly hypoelliptic if any local solution u of Lu = 0 is smooth. We allow for systems, i.e. the coefficients may be matrices, not necessarily of square size.
Bär, Christian
core
On a class of partially hypoelliptic microdifferential equations
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1987 Let M be a real analytic manifold with a complexification X. We consider the microdifferential equation defined in a neighborhood of \(\rho_ 0\in \dot T^*_ MX\) whose principal symbol is written in the form (1) \(p=p_ 1+\sqrt{-1}q_ 1^{2m}p_ 2\) in a neighborhood of \(\rho_ 0\in \dot T^*_ MX\).
Tose, Nobuyuki, Uchida, Moto-o
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Singular stochastic differential equations with elliptic and hypoelliptic diffusions [PDF]
, 2020 In this thesis, the well-posedness of stochastic differential equations (SDEs) with singular coefficients is discussed. First, it is proved that SDEs with elliptic diffusion possess a unique solution when drift vector fields belong to the Orlicz ...
Nam, Kyeongsik
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Parametric inference for hypoelliptic ergodic diffusions with full observations [PDF]
, 2020 International audienceMultidimensional hypoelliptic diffusions arise naturally in different fields, for example to model neuronal activity. Estimation in those models is complex because of the degenerate structure of the diffusion coefficient.
Melnykova, Anna
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Hypoelliptic Degenerate Evolution Equations of the Second Order
Publications of the Research Institute for Mathematical Sciences, 1975 For degenerate parabolic differential operators, the study of hypoellipticity has been made by many authors (see [1]~[9]). But for degenerate ]?-parabolie differential operators, its study has not been made so detailed (see F. Treves [10]). So we shall give a sufficient condition for the operator given by (0.1) to be hypoelliptic by constructing very ...
openaire +2 more sources
Solutions of logarithmic type for elliptic and hypoelliptic equations [PDF]
, 1996 LetP be an elliptic or hypoelliptic linear partial operator. We study the followingL1-BMO regularity problem: doesPu=f∈L1 implyu∈BMO?
M. Calanchi, N. Minh Tri, L. Rodino
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Gaussian estimates for hypoelliptic operators via optimal control [PDF]
, 2007 We obtain Gaussian lower bounds for the fundamental solution of a class of hypoelliptic equations, by using repeatedly an invariant Harnack inequality.
Ugo Boscain +2 more
core +1 more source
Higher-order hypoelliptic damped wave equations on graded Lie groups with data from negative order Sobolev spaces : the critical case [PDF]
Let G be a graded Lie group with homogeneous dimension . In this paper, we study the Cauchy problem for a semilinear hypoelliptic damped wave equation involving a positive Rockland operator R of homogeneous degree on G with power type nonlinearity and ...
Mondal, Shyam Swarup +3 more
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