929 research outputs found
Interpolation of Hilbert and Sobolev Spaces: Quantitative Estimates and Counterexamples
This paper provides an overview of interpolation of Banach and Hilbert
spaces, with a focus on establishing when equivalence of norms is in fact
equality of norms in the key results of the theory. (In brief, our conclusion
for the Hilbert space case is that, with the right normalisations, all the key
results hold with equality of norms.) In the final section we apply the Hilbert
space results to the Sobolev spaces and
, for and an open . We exhibit examples in one and two dimensions of sets
for which these scales of Sobolev spaces are not interpolation scales. In the
cases when they are interpolation scales (in particular, if is
Lipschitz) we exhibit examples that show that, in general, the interpolation
norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio
of these two norms can be arbitrarily large
Dynamic Transitions for Quasilinear Systems and Cahn-Hilliard equation with Onsager mobility
The main objectives of this article are two-fold. First, we study the effect
of the nonlinear Onsager mobility on the phase transition and on the
well-posedness of the Cahn-Hilliard equation modeling a binary system. It is
shown in particular that the dynamic transition is essentially independent of
the nonlinearity of the Onsager mobility. However, the nonlinearity of the
mobility does cause substantial technical difficulty for the well-posedness and
for carrying out the dynamic transition analysis. For this reason, as a second
objective, we introduce a systematic approach to deal with phase transition
problems modeled by quasilinear partial differential equation, following the
ideas of the dynamic transition theory developed recently by Ma and Wang
Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group
We study Sobolev-type metrics of fractional order on the group
\Diff_c(M) of compactly supported diffeomorphisms of a manifold . We show
that for the important special case the geodesic distance on
\Diff_c(S^1) vanishes if and only if . For other manifolds we
obtain a partial characterization: the geodesic distance on \Diff_c(M)
vanishes for and for ,
with being a compact Riemannian manifold. On the other hand the geodesic
distance on \Diff_c(M) is positive for and
.
For we discuss the geodesic equations for these metrics. For
we obtain some well known PDEs of hydrodynamics: Burgers' equation for ,
the modified Constantin-Lax-Majda equation for and the
Camassa-Holm equation for .Comment: 16 pages. Final versio
A Probabilistic proof of the breakdown of Besov regularity in -shaped domains
{We provide a probabilistic approach in order to investigate the smoothness
of the solution to the Poisson and Dirichlet problems in -shaped domains. In
particular, we obtain (probabilistic) integral representations for the
solution. We also recover Grisvard's classic result on the angle-dependent
breakdown of the regularity of the solution measured in a Besov scale
Boundary Conditions for Singular Perturbations of Self-Adjoint Operators
Let A:D(A)\subseteq\H\to\H be an injective self-adjoint operator and let
\tau:D(A)\to\X, X a Banach space, be a surjective linear map such that
\|\tau\phi\|_\X\le c \|A\phi\|_\H. Supposing that \text{\rm Range}
(\tau')\cap\H' =\{0\}, we define a family of self-adjoint
operators which are extensions of the symmetric operator .
Any in the operator domain is characterized by a sort
of boundary conditions on its univocally defined regular component \phireg,
which belongs to the completion of D(A) w.r.t. the norm \|A\phi\|_\H. These
boundary conditions are written in terms of the map , playing the role of
a trace (restriction) operator, as \tau\phireg=\Theta Q_\phi, the extension
parameter being a self-adjoint operator from X' to X. The self-adjoint
extension is then simply defined by A^\tau_\Theta\phi:=A \phireg. The case in
which is a convolution operator on LD, T a distribution with
compact support, is studied in detail.Comment: Revised version. To appear in Operator Theory: Advances and
Applications, vol. 13
Regularity of Ornstein-Uhlenbeck processes driven by a L{\'e}vy white noise
The paper is concerned with spatial and time regularity of solutions to
linear stochastic evolution equation perturbed by L\'evy white noise "obtained
by subordination of a Gaussian white noise". Sufficient conditions for spatial
continuity are derived. It is also shown that solutions do not have in general
\cadlag modifications. General results are applied to equations with fractional
Laplacian. Applications to Burgers stochastic equations are considered as well.Comment: This is an updated version of the same paper. In fact, it has already
been publishe
Fractional differentiability for solutions of nonlinear elliptic equations
We study nonlinear elliptic equations in divergence form
When
has linear growth in , and assuming that enjoys smoothness, local
well-posedness is found in for certain values of
and . In the particular case
, and ,
, we obtain for each
. Our main tool in the proof is a more general result, that
holds also if has growth in , , and
asserts local well-posedness in for each , provided that
satisfies a locally uniform condition
An online authoring and publishing platform for field guides and identification tools
Various implementation approaches are available for digital field
guides and identification tools that are created for the web and mobile devices.
The architecture of the âbiowikifarmâ publishing platform and some technical
and social advantages of a document- and author-centric approach based
on the MediaWiki open source software over custom-developed, database
driven software are presented
MART-1 peptide vaccination plus IMP321 (LAG-3Ig fusion protein) in patients receiving autologous PBMCs after lymphodepletion: results of a Phase I trial.
BACKGROUND: Immunotherapy offers a promising novel approach for the treatment of cancer and both adoptive T-cell transfer and immune modulation lead to regression of advanced melanoma. However, the potential synergy between these two strategies remains unclear.
METHODS: We investigated in 12 patients with advanced stage IV melanoma the effect of multiple MART-1 analog peptide vaccinations with (nâ=â6) or without (nâ=â6) IMP321 (LAG-3Ig fusion protein) as an adjuvant in combination with lymphodepleting chemotherapy and adoptive transfer of autologous PBMCs at day (D) 0 (Trial registration No: NCT00324623). All patients were selected on the basis of ex vivo detectable MART-1-specific CD8 T-cell responses and immunized at D0, 8, 15, 22, 28, 52, and 74 post-reinfusion.
RESULTS: After immunization, a significant expansion of MART-1-specific CD8 T cells was measured in 83% (nâ=â5/6) and 17% (nâ=â1/6) of patients from the IMP321 and control groups, respectively (Pâ<â0.02). Compared to the control group, the mean fold increase of MART-1-specific CD8 T cells in the IMP321 group was respectively >2-, >4- and >6-fold higher at D15, D30 and D60 (Pâ<â0.02). Long-lasting MART-1-specific CD8 T-cell responses were significantly associated with IMP321 (Pâ<â0.02). At the peak of the response, MART-1-specific CD8 T cells contained higher proportions of effector (CCR7â» CD45RAâș/â») cells in the IMP321 group (Pâ<â0.02) and showed no sign of exhaustion (i.e. were mostly PD1â»CD160â»TIM3â»LAG3â»2B4âș/â»). Moreover, IMP321 was associated with a significantly reduced expansion of regulatory T cells (Pâ<â0.04); consistently, we observed a negative correlation between the relative expansion of MART-1-specific CD8 T cells and of regulatory T cells. Finally, although there were no confirmed responses as per RECIST criteria, a transient, 30-day partial response was observed in a patient from the IMP321 group.
CONCLUSIONS: Vaccination with IMP321 as an adjuvant in combination with lymphodepleting chemotherapy and adoptive transfer of autologous PBMCs induced more robust and durable cellular antitumor immune responses, supporting further development of IMP321 as an adjuvant for future immunotherapeutic strategies
On the Fourier transform of the characteristic functions of domains with -smooth boundary
We consider domains with -smooth boundary and
study the following question: when the Fourier transform of the
characteristic function belongs to ?Comment: added two references; added footnotes on pages 6 and 1
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