500 research outputs found
A threshold phenomenon for embeddings of into Orlicz spaces
We consider a sequence of positive smooth critical points of the
Adams-Moser-Trudinger embedding of into Orlicz spaces. We study its
concentration-compactness behavior and show that if the sequence is not
precompact, then the liminf of the -norms of the functions is greater
than or equal to a positive geometric constant.Comment: 14 Page
The Construction of a Partially Regular Solution to the Landau-Lifshitz-Gilbert Equation in
We establish a framework to construct a global solution in the space of
finite energy to a general form of the Landau-Lifshitz-Gilbert equation in
. Our characterization yields a partially regular solution,
smooth away from a 2-dimensional locally finite Hausdorff measure set. This
construction relies on approximation by discretization, using the special
geometry to express an equivalent system whose highest order terms are linear
and the translation of the machinery of linear estimates on the fundamental
solution from the continuous setting into the discrete setting. This method is
quite general and accommodates more general geometries involving targets that
are compact smooth hypersurfaces.Comment: 43 pages, 2 figure
Quantization for an elliptic equation of order 2m with critical exponential non-linearity
On a smoothly bounded domain we consider a sequence of
positive solutions in to
the equation subject to Dirichlet
boundary conditions, where . Assuming that
we
prove that is an integer multiple of
\Lambda_1:=(2m-1)!\vol(S^{2m}), the total -curvature of the standard
-dimensional sphere.Comment: 33 page
Multiple solutions of the quasirelativistic Choquard equation
We prove existence of multiple solutions to the quasirelativistic Choquard equation with a scalar potential
Existence of solutions to a higher dimensional mean-field equation on manifolds
For we prove an existence result for the equation on a closed Riemannian
manifold of dimension for certain values of .Comment: 15 Page
On a functional satisfying a weak Palais-Smale condition
In this paper we study a quasilinear elliptic problem whose functional
satisfies a weak version of the well known Palais-Smale condition. An existence
result is proved under general assumptions on the nonlinearities.Comment: 18 page
Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system
We describe the asymptotic behavior as time goes to infinity of solutions of
the 2 dimensional corotational wave map system and of solutions to the 4
dimensional, radially symmetric Yang-Mills equation, in the critical energy
space, with data of energy smaller than or equal to a harmonic map of minimal
energy. An alternative holds: either the data is the harmonic map and the
soltuion is constant in time, or the solution scatters in infinite time
Small coupling limit and multiple solutions to the Dirichlet Problem for Yang Mills connections in 4 dimensions - Part I
In this paper (Part I) and its sequels (Part II and Part III), we analyze the
structure of the space of solutions to the epsilon-Dirichlet problem for the
Yang-Mills equations on the 4-dimensional disk, for small values of the
coupling constant epsilon. These are in one-to-one correspondence with
solutions to the Dirichlet problem for the Yang Mills equations, for small
boundary data. We prove the existence of multiple solutions, and, in
particular, non minimal ones, and establish a Morse Theory for this non-compact
variational problem. In part I, we describe the problem, state the main
theorems and do the first part of the proof. This consists in transforming the
problem into a finite dimensional problem, by seeking solutions that are
approximated by the connected sum of a minimal solution with an instanton, plus
a correction term due to the boundary. An auxiliary equation is introduced that
allows us to solve the problem orthogonally to the tangent space to the space
of approximate solutions. In Part II, the finite dimensional problem is solved
via the Ljusternik-Schirelman theory, and the existence proofs are completed.
In Part III, we prove that the space of gauge equivalence classes of Sobolev
connections with prescribed boundary value is a smooth manifold, as well as
some technical lemmas used in Part I. The methods employed still work when the
4-dimensional disk is replaced by a more general compact manifold with
boundary, and SU(2) is replaced by any compact Lie group
On Singularity formation for the L^2-critical Boson star equation
We prove a general, non-perturbative result about finite-time blowup
solutions for the -critical boson star equation in 3 space dimensions. Under
the sole assumption that the solution blows up in at finite time, we
show that has a unique weak limit in and that has a
unique weak limit in the sense of measures. Moreover, we prove that the
limiting measure exhibits minimal mass concentration. A central ingredient used
in the proof is a "finite speed of propagation" property, which puts a strong
rigidity on the blowup behavior of .
As the second main result, we prove that any radial finite-time blowup
solution converges strongly in away from the origin. For radial
solutions, this result establishes a large data blowup conjecture for the
-critical boson star equation, similar to a conjecture which was
originally formulated by F. Merle and P. Raphael for the -critical
nonlinear Schr\"odinger equation in [CMP 253 (2005), 675-704].
We also discuss some extensions of our results to other -critical
theories of gravitational collapse, in particular to critical Hartree-type
equations.Comment: 24 pages. Accepted in Nonlinearit
Distinguishing N-acetylneuraminic acid linkage isomers on glycopeptides by ion mobility-mass spectrometry
Differentiating the structure of isobaric glycopeptides represents a major
challenge for mass spectrometry-based characterisation techniques. Here we
show that the regiochemistry of the most common N-acetylneuraminic acid
linkages of N-glycans can be identified in a site-specific manner from
individual glycopeptides using ion mobility-mass spectrometry analysis of
diagnostic fragment ions
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