580 research outputs found
Yang-Mills fields on CR manifolds
We study pseudo Yang-Mills fields on a compact strictly pseudoconvex CR
manifold.Comment: 52 page
Levi umbilical surfaces in complex space
We define a complex connection on a real hypersurface of \C^{n+1} which is
naturally inherited from the ambient space. Using a system of Codazzi-type
equations, we classify connected real hypersurfaces in \C^{n+1}, ,
which are Levi umbilical and have non zero constant Levi curvature. It turns
out that such surfaces are contained either in a sphere or in the boundary of a
complex tube domain with spherical section.Comment: 18 page
The Deformation of an Elastic Substrate by a Three-Phase Contact Line
Young's classic analysis of the equilibrium of a three-phase contact line
ignores the out-of-plane component of the liquid-vapor surface tension. While
it has long been appreciated that this unresolved force must be balanced by
elastic deformation of the solid substrate, a definitive analysis has remained
elusive because conventional idealizations of the substrate imply a divergence
of stress at the contact line. While a number of theories of have been
presented to cut off the divergence, none of them have provided reasonable
agreement with experimental data. We measure surface and bulk deformation of a
thin elastic film near a three-phase contact line using fluorescence confocal
microscopy. The out-of-plane deformation is well fit by a linear elastic theory
incorporating an out-of-plane restoring force due to the surface tension of the
gel. This theory predicts that the deformation profile near the contact line is
scale-free and independent of the substrate elastic modulus.Comment: 4 pages, 3 figure
Resolvent Estimates in L^p for the Stokes Operator in Lipschitz Domains
We establish the resolvent estimates for the Stokes operator in
Lipschitz domains in , for . The result, in particular, implies that the Stokes operator in a
three-dimensional Lipschitz domain generates a bounded analytic semigroup in
for (3/2)-\varep < p< 3+\epsilon. This gives an affirmative answer to a
conjecture of M. Taylor.Comment: 28 page. Minor revision was made regarding the definition of the
Stokes operator in Lipschitz domain
Generalized Jacobi identities and ball-box theorem for horizontally regular vector fields
We consider a family of vector fields and we assume a horizontal regularity
on their derivatives. We discuss the notion of commutator showing that
different definitions agree. We apply our results to the proof of a ball-box
theorem and Poincar\'e inequality for nonsmooth H\"ormander vector fields.Comment: arXiv admin note: material from arXiv:1106.2410v1, now three separate
articles arXiv:1106.2410v2, arXiv:1201.5228, arXiv:1201.520
Analyticity of layer potentials and solvability of boundary value problems for divergence form elliptic equations with complex coefficients
We consider divergence form elliptic operators of the form L=-\dv
A(x)\nabla, defined in , ,
where the coefficient matrix is , uniformly
elliptic, complex and -independent. We show that for such operators,
boundedness and invertibility of the corresponding layer potential operators on
, is stable under
complex, perturbations of the coefficient matrix. Using a variant
of the Theorem, we also prove that the layer potentials are bounded and
invertible on whenever is real and symmetric (and
thus, by our stability result, also when is complex, is small enough and is real, symmetric,
and elliptic). In particular, we establish solvability of the Dirichlet and
Neumann (and Regularity) problems, with (resp. data, for
small complex perturbations of a real symmetric matrix. Previously,
solvability results for complex (or even real but non-symmetric) coefficients
were known to hold only for perturbations of constant matrices (and then only
for the Dirichlet problem), or in the special case that the coefficients
, , which corresponds to the Kato square
root problem
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