Results 51 to 60 of about 3,848 (132)
Hypoellipticity and Higher Order Levi Conditions
, 2014 We study the $C^\infty$-hypoellipticity for a class of double characteristic operators with simplectic characteristic manifold, in the case the classical condition of minimal loss of derivatives is ...
Mughetti, Marco
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Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.Abstract The aim of this paper is to prove the existence of Hadamard states for the Maxwell equations on any globally hyperbolic spacetime. This will be achieved by introducing a new gauge fixing condition, the Cauchy radiation gauge, that will allow to suppress all the unphysical degrees of freedom. The key ingredient for achieving this gauge is a new
Simone Murro, Gabriel Schmid
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$L^p$-parabolic regularity and non-degenerate Ornstein-Uhlenbeck type operators
, 2014 We prove $L^p$-parabolic a-priori estimates for $\partial_t u + \sum_{i,j=1}^d c_{ij}(t)\partial_{x_i x_j}^2 u = f $ on $R^{d+1}$ when the coefficients $c_{ij}$ are locally bounded functions on $R$.
Priola, Enrico
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On the properties of the symbols of one class of hypoelliptic equations
Sibirskii zhurnal industrial'noi matematiki, 2019 We consider regular hypoelliptic operators and study some properties of completely regular polyhedra. Basing on the obtained properties, we find an upper bound for the functional dimension of the solution spaces of hypoelliptic equations.
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On curvature bounds in Lorentzian length spaces
Journal of the London Mathematical Society, Volume 110, Issue 2, August 2024.Abstract We introduce several new notions of (sectional) curvature bounds for Lorentzian pre‐length spaces: On the one hand, we provide convexity/concavity conditions for the (modified) time separation function, and, on the other hand, we study four‐point conditions, which are suitable also for the non‐intrinsic setting. Via these concepts, we are able
Tobias Beran +2 more
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The Metivier inequality and ultradifferentiable hypoellipticity
Mathematische Nachrichten, Volume 297, Issue 7, Page 2517-2531, July 2024.Abstract In 1980, Métivier characterized the analytic (and Gevrey) hypoellipticity of L2$L^2$‐solvable partial linear differential operators by a priori estimates. In this note, we extend this characterization to ultradifferentiable hypoellipticity with respect to Denjoy–Carleman classes given by suitable weight sequences. We also discuss the case when
Paulo D. Cordaro, Stefan Fürdös
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Harnack inequalities for hypoelliptic evolution operators: geometric issues and applications
Bruno Pini Mathematical Analysis Seminar, 2012 We consider linear second order Partial Differential Equations in the form of "sum of squares of Hörmander vector fields plus a drift term" on a given domain.
Sergio Polidoro
doaj
Short-time asymptotics of the regularizing effect for semigroups generated by quadratic operators
, 2016 We study accretive quadratic operators with zero singular spaces. These degenerate non-selfadjoint differential operators are known to be hypoelliptic and to generate contraction semigroups which are smoothing in the Schwartz space for any positive time.
Hitrik, Michael +2 more
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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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Bulletin of the London Mathematical Society, Volume 56, Issue 3, Page 981-1003, March 2024.Abstract We study the linear relaxation Boltzmann equation on the torus with a spatially varying jump rate which can be zero on large sections of the domain. In Bernard and Salvarani (Arch. Ration. Mech. Anal. 208 (2013), no. 3, 977–984), Bernard and Salvarani showed that this equation converges exponentially fast to equilibrium if and only if the jump
Josephine Evans, Iván Moyano
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