bounds on coarsening rates for the lifschitz slyozov wagner equation this paper is concerned with the large time behavior of solutions to the lifschitz slyozov wagner lsw system of equations point wise in time upper and lower bounds on the rate of coarsening are obtained for solutions with fairly general initial data these bounds complement the time averaged upper bounds obtained by dai and pego and the point wise in time upper and lower bounds obtained by niethammer and velasquez for solutions with initial data close to a self similar solution

atomic and molecular decompositions of anisotropic besov spaces in this work we develop the theory of weighted anisotropic besov spaces associated with general expansive matrix dilations and doubling measures with the use of discrete wavelet transforms this study extends the isotropic littlewood paley methods of dyadic transforms of frazier and jawerth 19 21 to non isotropic settings

an introduction to mathematical models of coagulation fragmentation processes a discrete deterministic mean field approach abstract we summarise the properties and the fundamental mathematical results associated with basic models which describe coagulation and fragmentation processes in a deterministic manner and in which cluster size is a discrete quantity an integer multiple of some basic unit size in particular we discuss smoluchowski s equation for aggregation the becker doring model of simultaneous aggregation and fragmentation and more general models involving coagulation and fragmentation

the becker doring equations at large times and their connection with the lsw theory of coarsening a systematic procedure is given for obtaining the asymptotic late time behavior of the becker doring equations describing the time evolution of a population of clusters of particles in lowest order of approximation the distribution of the sizes of the largest clusters satisfies the equations of the lifshitz slyozov wagner theory of coarsening

a tower of coverings of quasi projective varieties abstract the main goal of this article is to relate asymptotic geometric properties on a tower of coverings of a non compact kahler manifold of finite volume with reasonable geometric assumptions to its universal covering examples to which our findings are applicable include moduli spaces of hyperbolic punctured riemann surfaces and hermitian locally symmetric spaces of finite volume

from the becker doring to the lifshitz slyozov wagner equations connections between two classical models of phase transitions the becker doring bd equations and the lifshitz slyozov wagner lsw equations are investigated homogeneous coefficients are considered and a scaling of the bd equations is introduced in the spirit of the previous works by penrose and collet goudon poupaud and vasseur convergence of the solutions to these rescaled bd equations towards a solution to the lsw equations is shown for general coefficients an approach in the spirit of numerical analysis allows to approximate the lsw equations by a sequence of bd equations a new uniqueness result for the bd equations is also provided

characterizations of weighted besov and triebel lizorkin spaces via temperatures abstract hardy littlewood type characterizations via temperatures on a half space of weighted besov and triebel lizorkin spaces studied recently by the author are given in the proof of the sufficient parts of the results a sub mean value property of temperatures is used in an elegant way to get control of certain terms by the hardy maximal function or its vector valued version as a byproduct of the results another characterization of weighted hardy spaces as well as characterizations of the gauss weierstrass integrals on a strip domain of distributions in the above weighted spaces is obtained also

a characterization of hajlasz sobolev and triebel lizorkin spaces via grand littlewood paley functions abstract in this paper we establish the equivalence between the hajlasz sobolev spaces or classical triebel lizorkin spaces and a class of grand triebel lizorkin spaces on euclidean spaces and also on metric spaces that are both doubling and reverse doubling in particular when p n n 1 we give a new characterization of the hajlasz sobolev spaces m 1 p r n via a grand littlewood paley function

decompositions of besov morrey spaces and triebel lizorkin morrey spaces the aim of this paper is to define the besov morrey spaces and the triebel lizorkin morrey spaces and to present a decomposition of functions belonging to these spaces our results contain an answer to the conjecture proposed by mazzucato

the becker doring equations and the lifshitz slyozov theory of coarsening in this paper the relation between the kinetic set of becker doring bd equations and the classical lifshitz slyozov ls theory of coarsening is studied a model that resembles the ls theory but keeps some of the nucleation effects is derived for this model a solution is described that shows how the kinetic effects explain the particular solution selected in the ls theory by means of a renormalization procedure a discrete group of transformations is shown to play an important role in describing the structure of the solution near the critical size of the ls theory

pointwise characterizations of besov and triebel lizorkin spaces and quasiconformal mappings abstract in this paper the authors characterize in terms of pointwise inequalities the classical besov spaces b p q s and triebel lizorkin spaces f p q s for all s 0 1 and p q n n s both in r n and in the metric measure spaces enjoying the doubling and reverse doubling properties applying this characterization the authors prove that quasiconformal mappings preserve f n s q s on r n for all s 0 1 and q n n s a metric measure space version of the above morphism property is also established

atomic and molecular decompositions of anisotropic triebel lizorkin spaces weighted anisotropic triebel lizorkin spaces are introduced and studied with the use of discrete wavelet transforms this study extends the isotropic methods of dyadic transforms of frazier and jawerth 1985 1989 to non isotropic settings associated with general expansive matrix dilations and a weights in close analogy with the isotropic theory we show that weighted anisotropic triebel lizorkin spaces are characterized by the magnitude of the transforms in appropriate sequence spaces we also introduce non isotropic analogues of the class of almost diagonal operators and we obtain atomic and molecular decompositions of these spaces thus extending isotropic results of frazier and jawerth

hardy spaces with variable exponents and generalized campanato spaces in the present paper we define hardy spaces with variable exponents on rn by the grand maximal function and then investigate their several properties the present paper will connect harmonic analysis with function spaces with variable exponents we obtain the atomic decomposition and the molecular decomposition with these decomposition proved we investigate the littlewood paley characterization also we specify the dual spaces of hardy spaces with variable exponents they will turn out to be campanato spaces with variable growth conditions the present paper covers local hardy spaces with variable exponents

decompositions of besov hausdorff and triebel lizorkin hausdorff spaces and their applications abstract let p 1 q 1 s r and 0 1 1 max p q in this paper the authors establish the transform characterizations of besov hausdorff spaces b h p q s r n and triebel lizorkin hausdorff spaces f h p q s r n q 1 as applications the authors then establish their embedding properties which on b h p q s r n is also sharp smooth atomic and molecular decomposition characterizations for suitable moreover using their atomic and molecular decomposition characterizations the authors investigate the trace properties and the boundedness of pseudo differential operators with homogeneous symbols in b h p q s r n and f h p q s r n q 1 which generalize the corresponding classical results on homogeneous besov and triebel lizorkin spaces when p 1 and q 1 by taking 0

fast reaction slow diffusion and curve shortening the reaction diffusion problem u 1 varepsilon delta u varepsilon 1 v n u quad u x 0 varepsilon g x quad partial n u 0 text on partial omega for a vector u x t varepsilon is considered in a domain omega in r m an asymptotic solution is constructed for varepsilon small it shows that at each x u tends quickly to a minimum of v u when v has several minima when u tends to a piecewise constant function boundary layer expansions are constructed around the resulting surfaces of discontinuity or fronts each front is found to move along its normal with a constant velocity determined by the discontinuity v in v across it when v 0 the front s normal velocity is varepsilon kappa where kappa is its mean curvature the motion of fronts in this manner is studied for arcs in the plane which are normal to partial omega at their endpoints and for fronts that are closed curves it is shown a front can shrink to a point in

a new class of function spaces connecting triebel lizorkin spaces and q spaces abstract let s r 0 p 1 and q 1 in this paper we introduce a new class of function spaces f p q s r n which unify and generalize the triebel lizorkin spaces with both p 1 and p and q spaces by establishing the carleson measure characterization of q space we then determine the relationship between triebel lizorkin spaces and q spaces which answers a question posed by dafni and xiao in g dafni j xiao some new tent spaces and duality theorem for fractional carleson measures and q r n j funct anal 208 2004 377 422 moreover via the hausdorff capacity we introduce a new class of tent spaces f t p q s r n 1 and determine their dual spaces f w p q s q r n where s r p q 1 max p q 1 0 q max p q and t denotes the conjugate index of t 1 as an application of this we further introduce certain hardy hausdorff spaces f h p q s r n and prove that the dual space of f h p q s r n is just f p q s q r n when p q 1

some remarks on large time asymptotic of the lifshitz slyozov equations we obtain an entropy functional for the lifshitz slyozov system this can be used to investigate the time asymptotics of the system in particular we describe situations in which the monomers concentration either tend to 0 or saturate as time becomes large the latter situation can be excluded under assumptions on the support of the initial data

on the stability in weak topology of the set of global solutions to the navier stokes equations let x be a suitable function space and let mathcal g subset x be the set of divergence free vector fields generating a global smooth solution to the incompressible homogeneous three dimensional navier stokes equations we prove that a sequence of divergence free vector fields converging in the sense of distributions to an element of mathcal g belongs to mathcal g if n is large enough provided the convergence holds anisotropically in frequency space typically this excludes self similar type convergence anisotropy appears as an important qualitative feature in the analysis of the navier stokes equations it is also shown that initial data which do not belong to mathcal g hence which produce a solution blowing up in finite time cannot have a strong anisotropy in their frequency support

a discrete transform and decompositions of distribution spaces abstract we study a representation formula of the form q q q for a distribution on r n this formula is obtained by discretizing and localizing a standard littlewood paley decomposition the map taking to the sequence q q with q running over the dyadic cubes in r n is called the transform the functions q and q have a particularly simple form moreover most of the familiar distribution spaces lp spaces 1 r n we also consider pointwise multipliers for the characteristic function of a domain we obtain boundedness results for a general class of domains which properly includes lipschitz domains several interpolation methods are easily analyzed via the sequence spaces for real interpolation we obtain among other things an extension to the case p 0 this in turn gives a new approach to the traditional atomic decomposition of hardy spaces

non uniform painless decompositions for anisotropic besov and triebel lizorkin spaces abstract in this article we construct affine systems that provide a simultaneous atomic decomposition for a wide class of functional spaces including the lebesgue spaces l p r d 1 p the novelty and difficulty of this construction is that we allow for non lattice translations we prove that for an arbitrary expansive matrix a and any set satisfying a certain spreadness condition but otherwise irregular there exists a smooth window whose translations along the elements of and dilations by powers of a provide an atomic decomposition for the whole range of the anisotropic triebel lizorkin spaces the generating window can be either chosen to be bandlimited or to have compact support to derive these results we start with a known general painless construction that has recently appeared in the literature we show that this construction extends to besov and triebel lizorkin spaces by providing adequate dual systems

the modified becker doring system with aggregation dominated rate coefficients we consider a system of becker doring equations modified in the manner of dreyer duderstadt 2006 j stat phys 123 55 we analyse the case of size independent rate coefficients in the case of weak fragmentation aggregation dominated we use matched asymptotic expansions to construct approximations to the cluster size distribution as it evolves from purely monomeric initial data to the equilibrium solution in which the typical cluster size is extremely large we compare the results with earlier calculations of a similar limit in the standard becker doring system and find a similar sequence of timescales with similar profile shapes however there are notable differences in the kinetic behaviour within timescales due to the modified system having a fragmentation rate which depends on the total number of clusters present in the system

canonical measures on metric graphs and a kazhdan s theorem we extend the notion of canonical measures to all possibly non compact metric graphs this will allow us to introduce a notion of hyperbolic measures on universal covers of metric graphs kazhdan s theorem for riemann surfaces describes the limiting behavior of canonical arakelov measures on finite covers in relation to the hyperbolic measure we will prove a generalized version of this theorem for metric graphs allowing any infinite galois cover to replace the universal cover we will show all such limiting measures satisfy a version of gauss bonnet formula which using the theory of von neumann dimensions can be interpreted as a trace formula in the special case where the infinite cover is the universal cover we will provide explicit methods to compute the corresponding limiting hyperbolic measure our ideas are motivated by non archimedean analytic and tropical geometry

slow passage through the nonhyperbolic homoclinic orbit associated with a subcritical pitchfork bifurcation for hamiltonian systems and the change in action slowly varying conservative systems are analyzed in the case of a reverse subcritical pitchfork bifurcation in which two saddles and a center coalesce before the bifurcation there is a hyperbolic double homoclinic orbit connecting a linear saddle point at the bifurcation a double nonhyperbolic homoclinic orbit connects to a nonlinear saddle point strongly nonlinear oscillations obtained by the method of averaging are not valid near unperturbed homoclinic orbits in the case in which the solution slowly passes through the nonhyperbolic homoclinic orbit associated with the subcritical pitchfork bifurcation the solution consists of a large sequence of nonhyperbolic homoclinic orbits connecting autonomous nonlinear saddle approaches solutions are captured into the left and right well phase jumps and the boundaries of the basins of attraction are computed it is shown that the change in action in the slow passage through the nonhyperbolic homoclinic orbits is much larger than the known change in action f

littlewood paley characterization and duality of weighted anisotropic product hardy spaces the authors study anisotropic product hardy spaces hwp a associated with a pair a a1 a2 of expansive dilations and a class of product muckenhoupt weights a a on rn rm this article is a continuation of their earlier work in bownik et al 2010 8 the authors establish the littlewood paley g function characterization and the transform characterization of hwp a 0 p 1 the authors also introduce the weighted anisotropic product campanato space lp w a and establish its transform characterization as an application the authors identify the dual space of hwp a with lp w a the results of this article improve the existing results for weighted product hardy spaces on r r and are new even in the weighted isotropic setting

duality and interpolation of anisotropic triebel lizorkin spaces we study properties of anisotropic triebel lizorkin spaces associated with general expansive dilations and doubling measures on mathbb r n using wavelet transforms this paper is a continuation of bownik in j geom anal 2007 to appear trans am math soc 358 1469 1510 2006 where we generalized the isotropic methods of dyadic varphi transforms of frazier and jawerth j funct anal 93 34 170 1990 to non isotropic settings by working at the level of sequence spaces we identify the duals of anisotropic triebel lizorkin spaces we also obtain several real and complex interpolation results for these spaces

calculus on arithmetic surfaces in a2 and a3 arakelov introduces an intersection calculus for arithmetic surfaces that is for stable models of curves over a number field in this paper we intend to show that his intersection product has a lot of useful properties more precisely we show that the following properties from the theory of algebraic surfaces have an analogue in our situation

new besov type spaces and triebel lizorkin type spaces including q spaces let s tau in mathbb r and q in 0 infty we introduce besov type spaces dot b s tau p q mathbb r n for p in 0 infty and triebel lizorkin type spaces dot f s tau p q mathbb r n rm for p in 0 infty which unify and generalize the besov spaces triebel lizorkin spaces and q spaces we then establish the varphi transform characterization of these new spaces in the sense of frazier and jawerth using the varphi transform characterization of dot b s tau p q mathbb r n rm and dot f s tau p q mathbb r n we obtain their embedding and lifting properties moreover for appropriate we also establish the smooth atomic and molecular decomposition characterizations of dot b s tau p q mathbb r n rm and dot f s tau p q mathbb r n for s in mathbb r p in 1 infty q in 1 infty and tau in 0 frac 1 max p q via the hausdorff capacity we introduce certain hardy hausdorff spaces b dot h s tau p q mathbb r n and prove that the dual space of b dot h s tau p q mathbb r n is just dot b s tau p q mathbb r n where t denotes the conjugate index of t in 1 infty

metastable states for the becker doring cluster equations the becker doring equations in whichc l t can represent the concentration ofl particle clusters or droplets in say a condensing vapour at timet are begin array 20 c dc l t mathord left vphantom dc l t dt right kern nulldelimiterspace dt j l 1 t j l t l 2 3 end array with j l t a l c 1 t c l t b l 1 c l 1 t and eitherc1 const case a or rho sum limits 1 infty lc l const case b the equilibrium solutions arec l q l z l where q l prod limits 2 l a r 1 mathord left vphantom a r 1 b r right kern nulldelimiterspace b r the density of the saturated vapour defined as rho s sum limits 1 infty lq l z s l wherez s is the radius of convergence of the series is assumed finite it is proved here that subject to some further plausible conditions on the kinetic coefficientsa l andb l there is a class of metastable solutions of the equations withc1 z s small and positive which take an exponentially long time to decay to their asymptotic steady states an exponentially long time means one that increases more rapidly than any negative power of the given value ofc1 z s or in caseb s as the latter tends to zero the main ingredients in the proof are i a time independent upper bound on the solution of the kinetic equations this upper bound is a steady state solution of case a of the equations of the type used in the becker doring theory of nucleation and ii an upper bound on the total concentration of particles in clusters greater than a certain critical size which with suitable initial conditions remains exponentially small until the time becomes exponentially large

anisotropic variable hardy lorentz spaces and their real interpolation abstract let p r n 0 be a variable exponent function satisfying the globally log holder continuous condition q 0 and a be a general expansive matrix on r n in this article the authors first introduce the anisotropic variable hardy lorentz space h a p q r n associated with a via the radial grand maximal function and then establish its radial or non tangential maximal function characterizations moreover the authors also obtain characterizations of h a p q r n respectively in terms of the atom and the lusin area function as an application the authors prove that the anisotropic variable hardy lorentz space h a p q r n serves as the intermediate space between the anisotropic variable hardy space h a p r n and the space l r n via the real interpolation this together with a special case of the real interpolation theorem of h kempka and j vybiral on the variable lorentz space further implies the coincidence between h a p q r n and the variable lorentz space l p q r n when ess inf x r n p x 1

front migration in the nonlinear cahn hilliard equation the method of matched asymptotic expansions is used to describe solutions of the nonlinear cahn hilliard equation for phase separation in n 1 space dimensions the expansion is formally valid when the thickness of internal transition layers is small compared with the distance separating layers and with their radii of curvature on the dominant slowest timescale the interface velocity is determined by the mean curvature of the interface by a non local relation which is identical to that in a well known quasi static model of solidification which exhibits a shape instability discovered by mullins sekerka j appl phys 34 323 329 1963 on a faster timescale the cahn hilliard equation regularizes a classic two phase stefan problem similarity solutions of the two phase stefan problem should describe boundary layers existence and uniqueness of such similarity solutions which admit metastable states is proved rigorously in an appendix

stability of the bergman kernel on a tower of coverings we obtain several results about stability of the bergman kernel on a tower of coverings on complex manifolds an effective estimate for stability of the bergman kernel is given for a tower of coverings on a compact riemann surface of genus geq 2 stability of the bergman kernel is established for towers of coverings on all hyperbolic riemann surfaces and on complete kahler manifolds that satisfy certain potential conditions as a consequence stability of the bergman kernel is established for any tower of coverings of riemann surfaces

asymptotic behaviour of solutions to the generalized becker doring equations for general initial data we prove the following asymptotic behaviour for solutions to the generalized becker doring system for general initial data under a detailed balance assumption and in situations where density is conserved in time there is a critical density s such that solutions with an initial density s converge strongly to the equilibrium with density and solutions with initial density s converge in a weak sense to the equilibrium with density s this extends the previous knowledge that this behaviour happens under more restrictive conditions on the initial data the main tool is a new estimate on the tail of solutions with density below the critical density

function spaces of variable smoothness and integrability abstract in this article we introduce triebel lizorkin spaces with variable smoothness and integrability our new scale covers spaces with variable exponent as well as spaces of variable smoothness that have been studied in recent years vector valued maximal inequalities do not work in the generality which we pursue and an alternate approach is thus developed using it we derive molecular and atomic decomposition results and show that our space is well defined i e independent of the choice of basis functions as in the classical case a unified scale of spaces permits clearer results in cases where smoothness and integrability interact such as sobolev embedding and trace theorems as an application of our decomposition we prove optimal trace theorem in the variable indices case

spectral theory of some degenerate elliptic operators with local singularities abstract this paper is based on our previous results haroske and skrzypczak 2008 23 haroske and skrzypczak in press 25 on compact embeddings of muckenhoupt weighted function spaces of besov and triebel lizorkin type with example weights of polynomial growth near infinity and near some local singularity our approach also extends haroske and triebel 1994 21 in various ways we obtain eigenvalue estimates of degenerate pseudodifferential operators of type b 2 p x d b 1 where b i l r i r n w i w i a i 1 2 and p x d 1 0 0 finally we deal with the negative spectrum of some operator h a v for where the potential v may have singularities in terms of muckenhoupt weights and a is a positive elliptic pseudodifferential operator of order 0 self adjoint in l 2 r n this part essentially relies on the birman schwinger principle we conclude this paper with a number of examples also comparing our results with preceding ones

characterizations of besov type and triebel lizorkin type spaces via maximal functions and local means abstract let s r in this paper the authors first establish the maximal function characterizations of the besov type space b p q s r n with p q 0 and 0 the triebel lizorkin type space f p q s r n with p 0 q 0 and 0 the besov hausdorff space b h p q s r n with p 1 q 1 and 0 1 max p q and the triebel lizorkin hausdorff space f h p q s r n with p q 1 and 0 1 max p q where t denotes the conjugate index of t 1 using this characterization the authors further obtain the local mean characterizations of these function spaces via functions satisfying the tauberian condition and establish a fourier multiplier theorem on these spaces all these results generalize the existing classical results on besov and triebel lizorkin spaces by taking 0 and are also new even for q spaces and hardy hausdorff spaces

on a thermodynamically consistent modification of the becker doring equations abstract recently dreyer and duderstadt have proposed a modification of the becker doring cluster equations which now have a different lyapunov function we start with existence and uniqueness results for the modified equations next we derive an explicit criterion for the existence of equilibrium states and solve the minimization problem for the lyapunov function finally we discuss the long time behavior in the case that equilibrium solutions do exist

on the growth of l 2 invariants for sequences of lattices in lie groups we study the asymptotic behaviour of betti numbers twisted torsion and other spectral invariants of sequences of locally symmetric spaces our main results are uniform versions of the degeorge wallach theorem of a theorem of delorme and various other limit multiplicity theorems a basic idea is to adapt the notion of benjamini schramm convergence bs convergence originally introduced for sequences of finite graphs of bounded degree to sequences of riemannian manifolds and analyze the possible limits we show that bs convergence of locally symmetric spaces g k implies convergence in an appropriate sense of the normalized relative plancherel measures associated to l2 g this then yields convergence of normalized multiplicities of unitary representations betti numbers and other spectral invariants on the other hand when the corresponding lie group g is simple and of real rank at least two we prove that there is only one possible bs limit i e when the volume tends to infinity locally symmetric spaces always bs converge to their universal cover g k this leads to various general uniform results when restricting to arbitrary sequences of congruence covers of a fixed arithmetic manifold we prove a strong quantitative version of bs convergence which in turn implies upper estimates on the rate of convergence of normalized betti numbers in the spirit of sarnak xue an important role in our approach is played by the notion of invariant random subgroups for higher rank simple lie groups g we exploit rigidity theory and in particular the nevo stuck zimmer theorem and kazhdan s property t to obtain a complete understanding of the space of irs s of g 2017 department of mathematics princeton university

new molecular characterizations of anisotropic musielak orlicz hardy spaces and their applications abstract let r n 0 0 be an anisotropic growth function and a a general expansive matrix on r n let h a r n be the anisotropic musielak orlicz hardy space associated with a defined via the non tangential grand maximal function in this article the authors establish a new molecular characterization of h a r n via its known atomic characterizations which positively answer a question mentioned by li et al 2016 34 as an application the authors obtain a criterion on the boundedness of linear operators on h a r n which further implies the boundedness of integral anisotropic calderon zygmund operators on h a r n in addition the boundedness of these operators from h a r n to the musielak orlicz space l r n is also presented

the becker doring cluster equations basic properties and asymptotic behaviour of solutions existence and uniqueness results are established for solutions to the becker doring cluster equations the density is shown to be a conserved quantity under hypotheses applying to a model of a quenched binary alloy the asymptotic behaviour of solutions with rapidly decaying initial data is determined denoting the set of equilibrium solutions byc 0 s the principal result is that if the initial density 0 s then the solution converges strongly toc o while if 0 s the solution converges weak toc s in the latter case the excess density 0 s corresponds to the formation of larger and larger clusters i e condensation the main tools for studying the asymptotic behaviour are the use of a lyapunov function with desirable continuity properties obtained from a known lyapunov function by the addition of a special multiple of the density and a maximum principle for solutions

asymptotic behaviour of solutions to the becker doring equations for arbitrary initial data on determine le comportement asymptotique des solutions des equations d amas de becker doring sous certaines hypotheses de decroissances sur les donnees initiales faites dans un article anterieur