Expand all Collapse all | Results 1 - 6 of 6 |
1. CJM 2013 (vol 65 pp. 740)
Regularization of Subsolutions in Discrete Weak KAM Theory We expose different methods of regularizations of subsolutions
in the context of discrete weak KAM theory.
They allow to prove the existence and the density of $C^{1,1}$
subsolutions. Moreover, these subsolutions can be made strict
and smooth outside of the Aubry set.
Keywords:discrete subsolutions, regularity Category:49C15 |
2. CJM 2012 (vol 65 pp. 702)
Regularity of Standing Waves on Lipschitz Domains We analyze the regularity of standing wave solutions
to nonlinear SchrÃ¶dinger equations of power type on bounded domains,
concentrating on Lipschitz domains. We establish optimal regularity results
in this setting, in Besov spaces and in HÃ¶lder spaces.
Keywords:standing waves, elliptic regularity, Lipschitz domain Categories:35J25, 35J65 |
3. CJM 2007 (vol 59 pp. 1207)
$H^p$-Maximal Regularity and Operator Valued Multipliers on Hardy Spaces We consider maximal regularity in the $H^p$ sense for the Cauchy
problem $u'(t) + Au(t) = f(t)\ (t\in \R)$, where $A$ is a closed
operator on a Banach space $X$ and $f$ is an $X$-valued function
defined on $\R$. We prove that if $X$ is an AUMD Banach space,
then $A$ satisfies $H^p$-maximal regularity if and only if $A$ is
Rademacher sectorial of type $<\frac{\pi}{2}$. Moreover we find an
operator $A$ with $H^p$-maximal regularity that does not have the
classical $L^p$-maximal regularity. We prove a related Mikhlin
type theorem for operator valued Fourier multipliers on Hardy
spaces $H^p(\R;X)$, in the case when $X$ is an AUMD Banach space.
Keywords:$L^p$-maximal regularity, $H^p$-maximal regularity, Rademacher boundedness Categories:42B30, 47D06 |
4. CJM 2007 (vol 59 pp. 1301)
Strichartz Inequalities for the Wave Equation with the Full Laplacian on the Heisenberg Group We prove dispersive and Strichartz inequalities for the solution of the wave
equation related to the full
Laplacian on the Heisenberg group, by means of Besov spaces defined by a
Littlewood--Paley
decomposition related to the spectral resolution of the full Laplacian.
This requires a careful
analysis due also to the non-homogeneous nature of the full Laplacian.
This result has to be compared to a previous one by Bahouri, G\'erard
and Xu concerning the solution of the wave equation related to
the Kohn Laplacian.
Keywords:nilpotent and solvable Lie groups, smoothness and regularity of solutions of PDEs Categories:22E25, 35B65 |
5. CJM 2005 (vol 57 pp. 771)
The Resolvent of Closed Extensions of Cone Differential Operators We study closed extensions $\underline A$ of
an elliptic differential operator $A$ on a manifold with conical
singularities, acting as an unbounded operator on a weighted $L_p$-space.
Under suitable conditions we show that the resolvent
$(\lambda-\underline A)^{-1}$ exists
in a sector of the complex plane and decays like $1/|\lambda|$ as
$|\lambda|\to\infty$. Moreover, we determine the structure of the resolvent
with enough precision to guarantee existence and boundedness of imaginary
powers of $\underline A$.
As an application we treat the Laplace--Beltrami operator for a metric with
straight conical degeneracy and describe domains yielding
maximal regularity for the Cauchy problem $\dot{u}-\Delta u=f$, $u(0)=0$.
Keywords:Manifolds with conical singularities, resolvent, maximal regularity Categories:35J70, 47A10, 58J40 |
6. CJM 2002 (vol 54 pp. 1121)
Fully Nonlinear Elliptic Equations on General Domains By means of the Pucci operator, we construct a function $u_0$, which plays
an essential role in our considerations, and give the existence and regularity
theorems for the bounded viscosity solutions of the generalized Dirichlet
problems of second order fully nonlinear elliptic equations on the general
bounded domains, which may be irregular. The approximation method, the accretive
operator technique and the Caffarelli's perturbation theory are used.
Keywords:Pucci operator, viscosity solution, existence, $C^{2,\psi}$ regularity, Dini condition, fully nonlinear equation, general domain, accretive operator, approximation lemma Categories:35D05, 35D10, 35J60, 35J67 |