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Some Properties of Solutions to Weakly Hypoelliptic Equations [PDF]
International Journal of Differential Equations, 2013 A linear different operator L is called weakly hypoelliptic if any local solution u of Lu=0 is smooth. We allow for systems, that is, the coefficients may be matrices, not necessarily of square size.
Christian Bär
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MULTI-TERM TIME-FRACTIONAL DERIVATIVE HEAT EQUATION FOR ONE-DIMENSIONAL DUNKL OPERATOR
Вестник КазНУ. Серия математика, механика, информатика, 2022 In this paper, we investigate the well-posedness for Cauchy problem for multi-term time-fractional heat equation associated with Dunkl operator. The equation under consideration includes a linear combination of Caputo derivatives in time with decreasing ...
D. Serikbaev
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Mathematics in Engineering, 2023 We consider nonlinear Kolmogorov-Fokker-Planck type equations of the form $ \begin{equation*} (\partial_t+X\cdot\nabla_Y)u = \nabla_X\cdot(A(\nabla_X u, X, Y, t)).
Prashanta Garain, Kaj Nyström
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Some global Sobolev inequalities related to Kolmogorov-type operators
Bruno Pini Mathematical Analysis Seminar, 2020 In this note we review a recent result in [17] in collaboration with N. Garofalo, where we establish global versions of Hardy-Littlewood-Sobolev inequalities attached to hypoelliptic equations of Kolmogorov type.
Giulio Tralli
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Comptes Rendus. Mathématique, 2020 We study the null-controllability of some hypoelliptic quadratic parabolic equations posed on the whole Euclidean space with moving control supports, and provide necessary or sufficient geometric conditions on the moving control supports to ensure null ...
Beauchard, Karine +2 more
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Hypoelliptic multiscale Langevin diffusions: Large deviations, invariant measures and small mass asymptotics [PDF]
, 2017 We consider a general class of non-gradient hypoelliptic Langevin diffusions and study two related questions. The first one is large deviations for hypoelliptic multiscale diffusions.
Hu, Wenqing, Spiliopoulos, Konstantinos
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Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term [PDF]
, 2005 We prove a Harnack inequality for the positive solutions of ultraparabolic equations of the type L u + V u= 0, where L is a linear second order hypoelliptic operator and V belongs to a class of functions of Stummel-Kato type.
Polidoro, Sergio +1 more
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On Liouville-type theorems and the uniqueness of the positive Cauchy problem for a class of hypoelliptic operators [PDF]
, 2015 This note contains a representation formula for positive solutions of linear degenerate second-order equations of the form $$ \partial_t u (x,t) = \sum_{j=1}^m X_j^2 u(x,t) + X_0 u(x,t) \qquad (x,t) \in \mathbb{R}^N \times\, ]- \infty ,T[,$$ proved by a ...
Kogoj, Alessia E. +2 more
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Bruno Pini Mathematical Analysis Seminar, 2016 For every bounded open set Ω in RN+1, we study the first boundary problem for a wide class of hypoelliptic evolution operators. The operators are assumed to be endowed with a well behaved global fundamental solution that allows us to construct a ...
Alessia E. Kogoj
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Hypoelliptic functional inequalities [PDF]
, 2018 In this paper we derive a variety of functional inequalities for general homogeneous invariant hypoelliptic differential operators on nilpotent Lie groups.
Ruzhansky, Michael +1 more
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