Results 41 to 50 of about 109 (95)
Harnack estimates for degenerate parabolic equations modeled on the subelliptic p -Laplacian
Advances in Mathematics, 2014 We establish a Harnack inequality for a class of quasi-linear PDE modeled on the prototype {equation*} \partial_tu= -\sum_{i=1}^{m}X_i^\ast (|\X u|^{p-2} X_i u){equation*} where $p\ge 2$, $ \ \X = (X_1,..., X_m)$ is a system of Lipschitz vector fields defined on a smooth manifold $\M$ endowed with a Borel measure $μ$, and $X_i^*$ denotes the adjoint of
Capogna, Luca +4 more
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Boundary regularity for subelliptic equations in the Heisenberg group
35 pages, comments ...
Abedin, Farhan, Tralli, Giulio
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Nonlinear subelliptic Schrödinger equations with external magnetic field
Electronic Journal of Differential Equations, 2004 Summary: To account for an external magnetic field in a Hamiltonian of a quantum system on a manifold (modelled here by a subelliptic Dirichlet form), one replaces the the momentum operator \(\frac 1i d\) in the subelliptic symbol by \(\frac 1i d-\alpha\), where \(\alpha\in TM^*\) is called a magnetic potential for the magnetic field \(\beta=d\alpha\).
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Subelliptic Hamilton-Jacobi equations: the coercive stationary case
Rendiconti Lincei, Matematica e Applicazioni, 2010 We prove the existence uniqueness and comparison results for a (Lipschitz) viscosity solution for an Hamilton−Jacobi equation on a Carnot group.
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Comparison Principles for subelliptic equations of Monge-Ampere type
, 2008 We present two comparison principles for viscosity sub- and supersolutions of Monge-Ampere-type equations associated to a family of vector fields. In particular, we obtain the uniqueness of a viscosity solution to the Dirichlet problem for the equation of prescribed horizontal Gauss curvature in a Carnot group.
BARDI, MARTINO, MANNUCCI, PAOLA
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Exact observability properties of subelliptic wave and Schrödinger equations
Séminaire de théorie spectrale et géométrieIn this survey paper, we report on recent works concerning exact observability (and, by duality, exact controllability) properties of subelliptic wave and Schrödinger-type equations. These results illustrate the slowdown of propagation in directions transverse to the horizontal distribution.
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On positivity of certain systems of partial differential equations. [PDF]
Proc Natl Acad Sci U S A, 2007 Parmeggiani A.
europepmc +1 more source
Guide to nonlinear potential estimates. [PDF]
Bull Math Sci, 2014 Kuusi T, Mingione G.
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Multiplier ideal sheaves and existence of Kähler-Einstein metrics of positive scalar curvature. [PDF]
Proc Natl Acad Sci U S A, 1989 Nadel AM.
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