maximal parabolic regularity for divergence operators including mixed boundary conditions abstract we show that elliptic second order operators a of divergence type fulfill maximal parabolic regularity on distribution spaces even if the underlying domain is highly non smooth the coefficients of a are discontinuous and a is complemented with mixed boundary conditions applications to quasilinear parabolic equations with non smooth data are presented

abstract quasilinear parabolic equations on considere des problemes paraboliques quasi lineaires abstraits p 0 u t a t u t u t f t u t t 0 u o u 0 ou u t est une fonction a valeurs dans un espace de banach x on donne des theoremes d existence locale et d unicite pour des solutions classiques et strictes de p 0

global solutions to semilinear parabolic systems for small data abstract we consider semilinear parabolic systems u t au f u g u 0 u 0 a being the generator of an analytic semigroup with spectrum a in the right half plane for appropriate small data g u 0 global solutions are obtained if 0 belongs to the resolvent set and local existence is proved if 0 a the inverse function theorem is used in a class of functions which are holder continuous with respect to time t the asymptotic behaviour of the solution is given too as a first application we prove the existence of global respectively local solutions to the navier stokes equations in l spaces in bounded respectively unbounded domains second we consider the case where a is an elliptic operator of order 2 m and f has bounded growth third a quasilinear example where the nonlinearity involves derivatives of the same order as a is studied then an example of a nonautonomous nonlinearity is given and finally the convergence of solutions of the time dependent system to solutions of the stationary semilinear elliptic one is derived for 0 a

holder classes with boundary conditions as interpolation spaces on etudie la caracterisation de certains espaces d interpolation reels entre le domaine d un operateur differentiel elliptique avec des conditions aux limites generales et l espace de banach de fonctions continues dans lequel le domaine est plonge

transmission problems in a thin layer set in the framework of the holder spaces resolution and impedance concept abstract we consider a family of singular transmission problems depending on some small positive parameter set in the juxtaposition of two rectangular domains they are written in the form of abstract elliptic equations and the study here is given in the holder spaces completing in this way the work in lp cases given in a favini r labbas k lemrabet s maingot study of the limit of transmission problems in a thin layer by the sum theory of linear operators rev mat complut 18 1 2005 143 176 in this first part we present a new approach for the resolution of these problems by using the concept of impedance operator this method is different of the one performing a rescaling in the thin layer see a favini r labbas k lemrabet s maingot study of the limit of transmission problems in a thin layer by the sum theory of linear operators rev mat complut 18 1 2005 143 176 it leads to obtain direct and simplified problems we use the dunford calculus and some techniques similar to that in r labbas problemes aux limites pour une equation differentielle abstraite de type elliptique these d etat universite de nice 1987 a favini r labbas s maingot h tanabe a yagi unified study of elliptic problems in holder spaces c r math acad sci paris 134 2005 g dore a favini r labbas k lemrabet s maingot a transmission problem in a thin layer part i sharp estimates in press to prove existence uniqueness results and some specific estimates on the impedance operator this study will allow us in a forthcoming work to obtain respectively optimal regularities and the limit problem when 0

a high capacity reversible watermarking approach for authenticating images exploiting down sampling histogram processing and block selection amongst the various data hiding schemes lossless data hiding has achieved substantial attention in the recent years lossless watermarking also known as reversible watermarking not only ensures the extraction of the hidden information called watermark but also the complete recovery of the original image as well recently several interesting reversible block based watermarking approaches using histogram processing have been reported these approaches offer substantial watermarking capacity for a fixed image quality measure however there is considerable margin of improvement as regards the imperceptibility versus capacity tradeoff is concerned some of the watermarking applications such as those related to integrity control need high capacity therefore we present a high capacity reversible watermarking approach based on histogram processing and block selection rw hpbs the proposed rw hpbs approach exploits the concept of down sampling for effectively increasing the capacity and is useful for integrity control and authentication related applications two down sampled versions the reference and the data hiding are obtained to create space for embedding authentication property is achieved by taking a secondary advantage of the location map before being compressed and embedded as an auxiliary information the effectiveness of the proposed method is shown through comparison with the existing techniques experimental results show that the proposed rw hpbs approach provides better imperceptibility versus capacity tradeoff and can detect tampering and collage attack

dynamic theory of quasilinear parabolic equations i abstracts evolution equations on etablit les fondements abstraits pour une theorie dynamique generale pour des problemes aux valeurs limites et initiales quasilineaires

stationary navier stokes equations with critically singular external forces existence and stability results abstract we show the unique existence of solutions to stationary navier stokes equations with small singular external forces belonging to a critical space to the best of our knowledge this is the largest critical space that is available up until now for this kind of existence this result can be viewed as the stationary counterpart of the existence result obtained by h koch and d tataru for the free non stationary navier stokes equations with initial data in bmo 1 the stability of the stationary solutions in such spaces is also obtained by a series of sharp estimates for resolvents of a singularly perturbed operator and the corresponding semigroup

nonlinear analytic semiflows in this paper a local existence and regularity theory is given for nonlinear parabolic initial value problems x t f x t and quasilinear initial value problems x t a x t x t f x t this theory extends the theory of daprato and grisvard of 1979 and shows how various properties like analyticity of solutions can be derived as a direct corollary of the existence theorem

recurrent traveling waves in a two dimensional saw toothed cylinder and their average speed abstract we study a curvature dependent motion of plane curves in a two dimensional infinite cylinder with spatially undulating boundary the law of motion is given by v a where v is the normal velocity of the curve is the curvature and a is a positive constant the boundary undulation is assumed to be almost periodic or more generally recurrent in a certain sense we first introduce the definition of recurrent traveling waves and establish a necessary and sufficient condition for the existence of such traveling waves we then show that the traveling wave is asymptotically stable if it exists next we show that a regular traveling wave has a well defined average speed if the boundary shape is strictly ergodic finally we study what we call virtual pinning which means that the traveling wave propagates over the entire cylinder with zero average speed such a peculiar situation can occur only in non periodic environments and never occurs if the boundary undulation is periodic

flattening of cr singular points and analyticity of the local hull of holomorphy i this is the first article of the two papers in which we investigate the holomorphic and formal flattening problem for a codimension two real submanifold in mathbb c n with n ge 3 near a non degenerate cr singular point the problem is motivated from the study of the complex plateau problem that seeks for the levi flat hypersurface bounded by a given real submanifold and is motivated by the classical complex analysis problem of finding the local hull of holomorphy of a real submanifold in a complex space the present article is focused on the case of cr singular points with at least one elliptic direction we solve the holomorphic flattening problem and thus provide a complete description of the local hull of holomorphy in this setting the results in this paper and those in flattening of cr singular points and analyticity of the local hull of holomorphy ii p 60 2014 are taken from our arxiv post flattening of cr singular points and analyticity of the local hull of holomorphy 2012 we split flattening of cr singular points and analyticity of the local hull of holomorphy 2012 into two independent articles to avoid it being too long

on a class of retarded partial differential equations on developpe des resultats recents sur des equations d evolution abstraites afin de les appliquer a un type d equations dans des espaces de banach avec un retard discret et continu ces equations peuvent etre considerees comme la version abstraite d equations integrodifferentielles partielles a retard

global solutions of abstract quasilinear parabolic equations abstract local and global existence and uniqueness for strict solutions of abstract quasilinear parabolic equations are studied applications to quasilinear parabolic partial differential equations are also given

flattening of cr singular points and analyticity of the local hull of holomorphy ii abstract this is the second article of the two papers in which we investigate the holomorphic and formal flattening problem of a non degenerate cr singular point of a codimension two real submanifold in c n with n 3 the problem is motivated from the study of the complex plateau problem that looks for the levi flat hypersurface bounded by a given real submanifold and by the classical complex analysis problem of finding the local hull of holomorphy of a real submanifold in a complex space the present article is focused on non degenerate flat cr singular points with at least one non parabolic bishop invariant we will solve the formal flattening problem in this setting the results in this paper and those in 23 are taken from our earlier arxiv post 22 we split 22 into two independent articles to avoid it being too long

stability of runge kutta methods for quasilinear parabolic problems we consider a quasilinear parabolic problem u t q u t u t u t 0 u 0 d where q w d c x x w w c x is a family of sectorial operators in a banach space x with fixed domain d this problem is discretized in time by means of a strongly a stable 0 2 runge kutta method we prove that the resulting discretization is stable under some natural assumptions on the dependence of q w with respect to w our results are useful for studying in l p norms 1 p many problems arising in applications some auxiliary results for time dependent parabolic problems are also provided

quasilinear systems with memory kernels we consider a quasilinear integrodifferential system in non normal form such a system is a generalization of a phase field model with memory and includes as a particular case the system describing the combustion of a material with memory in this paper we study both the direct and the inverse problems our fundamental tools are the theory of analytic semigroups optimal regularity results and fixed point arguments

analysis of fully discrete approximations to parabolic problems with rough or distribution valued initial data we consider fully discrete approximations to a parabolic initial boundary value problem with rough or distribution valued initial data in two space dimensions for discretization in time and space we apply single step methods and the standard galerkin method with piecewise linear test functions respectively for spatial discretization of the initial condition we are however forced to use more involved constructions our main result is stability and error estimates of the discrete solutions

stability in a two dimensional free boundary combustion model we prove rigorously the stability of the planar travelling wave solution to a free boundary system in r2 arising as a model in combustion theory for appropriate values of the reduced lewis number after changements of coordinates and unknowns the problem is reduced to the stability of the null solution of a fixed boundary parabolic system the difficulties consist in the fact that the final system is fully nonlinear and the spectrum of the linearized system contains the halffine 0 they are overcome setting the problem in a suitably weighted holder space

a new numerical method for backward parabolic problems in the maximum norm setting a new method for solving numerically backward parabolic problems is proposed as usual for this kind of ill posed problems it is assumed that an a priori bound for the solution is available the algorithm consists of two basic steps first a standard forward integration is performed in order to approximate the solution at suitable future time levels second a holomorphic recovery procedure is carried out providing the required approximations for the preceding times the analysis is valid in the maximum norm setting and rigorous estimates are derived among other advantages the method can also be applied to nonlinear problems and it produces a continuous output some numerical illustrations are presented

direct and inverse problems for a phase field model with memory we consider a semilinear integrodifferential system in non normal form such a system is a generalization of the one that arises in the phase field theory with memory we prove an abstract existence and uniqueness theorem and a continuous dependence result for the direct problem reformulating the direct problem in a suitable way we prove that the identification problem admits a unique solution

asymptotic expansion for layer solutions of a singularly perturbed reaction diffusion system for a singularly perturbed n dimensional system of reactiondiffusion equations assuming that the 0th order solutions possess boundary and internal layers and are stable in each regular and singular region we construct matched asymptotic expansions for formal solutions in all the regular boundary internal and initial layers to any desired order in e the formal solution shows that there is an invariant manifold of wave front like solutions that attracts other nearby solutions we also give conditions for the wave front like solutions to converge slowly to stationary solutions on that manifold

regular solutions for time dependent abstract integrodifferential equations with singular kernel abstract results of existence uniqueness and regularity for strict and classical solutions of linear nonautonomous integrodifferential initial value problems are proved using maximal regularity properties for the autonomous nonintegral case

on the solutions of the first boundary value problem for the linear parabolic equations on etudie le premier probleme aux valeurs limites pour une equation parabolique lineaire d ordre 2 sous l hypothese que le terme inhomogene est continu en espace et en temps et continu de holder seulement par rapport aux variables d espace

quasilinear evolution equations and parabolic systems it is shown that general quasilinear parabolic systems possess unique maximal classical solutions for sufficiently smooth initial values provided the boundary conditions are time independent moreover it is shown that in the autonomous case these equations generate local semi flows on appropriate sobolev spaces our results apply in particular to the case of prescribed boundary values dirichlet boundary conditions

on the abstract cauchy problem of parabolic type in spaces of continuous functions on etudie l existence l unicite et les proprietes de regularite des solutions du probleme de cauchy u t au r f t o t t u o u 0 ou a d a ce e est un operateur lineaire clos dans l espace de banach e

holder regularity in variational parabolic non homogeneous equations abstract we prove optimal holder regularity results for the solutions to second order variational parabolic equations with holder continuous coefficients and non homogeneous boundary data using analytic semigroups methods

recovering a leading coefficient and a memory kernel in first order integro differential operator equations abstract we are concerned with the identification of the scalar functions a and k in the convolution first order integro differential equation u t a t au t k bu t f t 0 t t k v t 0 t k t s v s ds in a banach space x where a and b are linear closed operators in x a being the generator of an analytic semigroup of linear bounded operators taking advantage of two pieces of additional information we can recover under suitable assumptions and locally in time both the unknown functions a and k the results so obtained are applied to an n dimensional integro differential identification problem in a bounded domain in r n

equivalences of real submanifolds in complex space we show that for any real analytic submanifold m in cn there is a proper real analytic subvariety v m such that for any p m v any real analytic submanifold min cn and any p m the germs m p and m p of the submanifolds m and mat p and prespectively are formally equivalent if and only if they are biholomorphically equivalent as an ap plication for p m v the problem of biholomorphic equivalence of the germs m p and m p is reduced to that of solving a system of polyno mial equations more general results for k equivalences are also stated and proved

maximum norm analysis of completely discrete finite element methods for parabolic problems we consider full discretizations of linear parabolic initial value problems in any space dimension finite elements are used for the discretization in space the resulting semidiscrete problem is integrated in time by means of a strongly a theta acceptable rational method stability estimates are derived and error bounds are established in the maximum norm for both smooth and rough initial data

robust and blind image watermarking in dct domain using inter block coefficient correlation abstract this study presents a robust and transparent watermarking method that exploits block based discrete cosine transform dct coefficient modification the difference in the dct coefficients of two blocks is calculated and modified based on the watermark bit to adjust this difference to a predefined range the first coefficient in the upper left corner of the array basis function is known as the direct current dc coefficient whereas the remainder includes the alternating current ac coefficients the extent of the dct coefficient modifications depends on the dc coefficient and median of the ac coefficients ordered by a zig zag sequence the robustness of the proposed method against various attacks was evaluated experimentally and experimental results demonstrate that the proposed method possesses great robustness against various single and combined attacks

global existence of solutions for a strongly coupled quasilinear parabolic system we are interested in existence uniqueness and a priori estimates of non negative solutions to the following problem begin gathered u t delta left left 1 alpha v right u right uf u v hfill v t delta v vg u v quad in 0 infty times omega hfill u v 0 quad in 0 infty times partial omega hfill u 0 u 0 v 0 v 0 quad in omega hfill end gathered 1 0

cα regularity for non autonomous linear integrodifferential equations of parabolic type abstract linear integrodifferential equations in general banach space are studied and applications are given to linear integrodifferential partial differential equations

analyticity of the maximal solution of an abstract nonlinear parabolic equation where u t x 0 7 j x r r satisfies other suitable conditions problem p is studied under the assumption that af au generates an analytic semigroup in e and has domain f which corresponds to a parabolicity condition on equation p problems of this kind have been studied by monotonicity methods see brezis 111 crandall ligget 3 and crandall pazy 4 to obtain global but weak solutions of p here we find a maximally defined strict solution by means of a linearization method and by virtue of maximal regularity results for the linear case this method has been used by da prato grisvard in 5 to obtain strict solutions of p with arguments which seem to be more simple and suitable to our purpose we get also the analyticity of u with respect to 1 w when f is analytic in section 1 some notation and assumptions are given problem p is studied in section 2 where we prove existence and uniqueness of the strict solution of p which is defined on a maximal time interval contained in 0 t and it is continuous with respect to t 0 in section 3 we give conditions to get global existence of the solution in section 4 we study analyticity with respect to t ug of the maximally defined solution of p and in section 5 a simple example is given in a subsequent paper we will show how this theory applies to the study of the analyttctty of the solutions of nonlinear parabol ic partial differential equations in spaces of holder continuous functions

on linear volterra equations of parabolic type in banach spaces linear integrodifferential equations of volterra type in a banach space are studied in case the main part of the equation generates an analytic co semigroup under very general assumptions it is shown that a resolvent operator exists and that many of the solution properties of parabolic evolu tion equations are inherited the results are then applied to integro partial differential equations of parabolic type

analytic semigroups generated by ultraweak operators let be a regular open subset of r n we present an improved generation result for nonvariational operators in l 1 this result is obtained by studying ultraweak operators and by proving generation of analytic semigroups in l p l p and in we also characterise interpolation and extrapolation spaces

formal and finite order equivalences we show that two families of germs of real analytic subsets in mathbb c n are formally equivalent if and only if they are equivalent of any finite order we further apply the same technique to obtain analogous statements for equivalences of real analytic self maps and vector fields under conjugations on the other hand we provide an example of two sets of germs of smooth curves that are equivalent of any finite order but not formally equivalent

on the continuity of ornstein uhlenbeck processes in infinite dimensions existence and continuity of ornstein uhlenbeck processes in banach and hilbert spaces are investigated under various assumptions

non explosion boundedness and ergodicity for stochastic semilinear equations abstract sufficient conditions for non explosion boundedness and ergodicity of solutions of a class of semilinear stochastic equations are given applications of the results are based on a new regularity theorem for solutions of the linear problem

convergence and finite determination of formal cr mappings in this paper we study the convergence and finite determination of formal holomorphic mappings of c 0 taking one real submanifold into another by a formal holomorphic mapping h c 0 c 0 we mean an n vector h h1 hn where each hj is a formal power series in n indeterminates with no constant term if m and m are real smooth submanifolds through 0 in c defined near the origin by z z 0 and z z 0 respectively where and are vector valued smooth defining functions then we say that a formal mapping h c 0 c 0 sends m into m if the vector valued power series h z h z is a matrix multiple of z z for real analytic hypersurfaces we shall prove the following theorem 1 let m and m be real analytic hypersurfaces through the origin in c n 2 assume that neither m nor m contains a nontrivial holomorphic subvariety through 0 then any formal mapping h c 0 c 0 sending m into m is convergent the condition that m above does not contain a nontrivial holomorphic subvariety is necessary see remark 2 3 as a corollary we obtain the following characterization

robust watermarking against geometric attacks using partial calculation of radial moments and interval phase modulation this paper presents a new image watermarking scheme which is blind and robust against geometric attacks the proposed algorithm is based on the features of radial moments in this algorithm the radial moments were first computed and then the watermark was embedded into the differential phase of various blocks of the original image using a special type of psk modulation called interval phase modulation ipm in order to embed the watermark into the phase of moments a particular method namely the partial calculation of moments was utilized for computation the implementation results show the improvement in the robustness and quality of the watermarked images in comparison with other methods

a bishop surface with a vanishing bishop invariant we give a solution to the equivalence problem for bishop surfaces with the bishop invariant 0 as a consequence we answer in the negative a problem that moser asked in 1985 after his work with webster in 1983 and his own work in 1985 this will be done in two major steps we first derive the formal normal form for such surfaces we then show that two real analytic bishop surfaces with 0 are holomorphically equivalent if and only if they have the same formal normal form up to a trivial rotation our normal form is constructed by an induction procedure through a completely new weighting system from what is used in the literature our convergence proof is done through a new hyperbolic geometry associated with the surface

on the evolution operator for a class of non autonomous abstract parabolic equations abstract we state existence and several properties of the evolution operator relevant to a family a t 0 t t of generators of analytic semigroups in a banach space the assumption that certain interpolation spaces do not depend on t allows us to weaken the usual regularity hypotheses on t a t requiring only continuity in suitable topologies