Results 11 to 20 of about 229 (132)

Subelliptic Wave Equations with Log-Lipschitz coefficients [PDF]

, 2020
In this paper we study the Cauchy problem for the wave equations for sums of squares of left invariant vector fields on compact Lie groups and also for hypoelliptic homogeneous left-invariant differential operators on graded Lie groups (the positive Rockland operators), when the time-dependent propagation speed satisfies a Log-Lipschitz condition.
Carlos Andres Rodriguez Torijano, Michael Ruzhansky   +1 more
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Harnack estimates for degenerate parabolic equations modeled on the\n subelliptic p-Laplacian [PDF]

Advances in Mathematics, 2013
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 $ $, and $X_i^*$ denotes the adjoint ...
Benny Avelin, Luca Capogna, Giovanna Citti, Kaj Nyström   +3 more
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Regularity of subelliptic Monge-Ampère equations in the plane [PDF]

Transactions of the American Mathematical Society, 2009
We establish a C ∞ C^\infty regularity result for C 1 , 1 C^{1,1} solutions of degenerate Monge-Ampère equation in R 2 \mathbb R^2 , under the assumption that the trace of the Hessian is bounded from
Pengfei Guan, Eric T. Sawyer
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Exact observability properties of subelliptic wave and Schrödinger equations

Séminaire de théorie spectrale et géométrie
In 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.
Cyril Letrouit
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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.
Marco Biroli
  +7 more sources

Positive Solution of a Subelliptic Nonlinear Equation on the Heisenberg Group [PDF]

Canadian Mathematical Bulletin, 2001
AbstractIn this paper, we establish the existence of positive solution of a nonlinear subelliptic equation involving the critical Sobolev exponent on the Heisenberg group, which generalizes a result of Brezis and Nirenberg in the Euclidean case.
Wei Wang
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Convexity of average operators for subsolutions to subelliptic equations [PDF]

Analysis & PDE, 2014
We study convexity properties of the average integral operators naturally associated with divergence-form second-order subelliptic operators ℒ with nonnegative characteristic form. When ℒ is the classical Laplace operator, these average operators are the usual average integrals over Euclidean spheres.
Andrea Bonfiglioli, Ermanno Lanconelli, Andrea Tommasoli   +2 more
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Regularity at the boundary for solutions of nonlinear subelliptic equations [PDF]

Indiana University Mathematics Journal, 1995
We establish an estimate, in terms of subelliptic \(p\)-capacity, for the modulus of continuity at the boundary of the solution to the Dirichlet problem associated to a class of subelliptic equations. We infer from it the sufficiency part of a Wiener type criterion for the regularity of boundary points.
Donatella Danielli
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Comparison Principles for subelliptic equations of Monge-Ampere type [PDF]

, 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.
Martino Bardi, Paola Mannucci
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Boundary regularity for subelliptic equations in the Heisenberg group [PDF]

35 pages, comments ...
Farhan Abedin, Giulio Tralli
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