evolutionary subgradient inclusions with nonlinear weakly continuous operators and applications abstract in this paper we consider the first order evolutionary inclusions with nonlinear weakly continuous operators and a multivalued term which involves the clarke subgradient of a locally lipschitz function first we provide a surjectivity result for stationary inclusion with weakly weakly upper semicontinuous multifunction then we use this result to prove the existence of solutions to the rothe sequence and the evolutionary subgradient inclusion finally we apply our results to the non stationary navier stokes equation with nonmonotone and multivalued frictional boundary conditions

the classification of automorphism groups of rational elliptic surfaces with section abstract in this paper we give a classification of regular automorphism groups of relatively minimal rational elliptic surfaces with section over the field c which have non constant j maps the automorphism group aut b of such a surface b is the semi direct product of its mordell weil group mw b and the subgroup aut b of the automorphisms preserving the zero section of the rational elliptic surface b the configuration of singular fibers on the surface determines the mordell weil group as has been shown by oguiso and shioda 1991 and aut b also depends on the singular fibers the classification of automorphism groups in this paper gives the group aut b in terms of the configuration of singular fibers on the surface in general aut b is a finite group of order less than or equal to 24 which is a z 2 z extension of either z n z z 2 z z 2 z d n the dihedral group of order 2n or a 4 the alternating group of order 12 the configuration of singular fibers does not determine the group aut b uniquely however we list explicitly all the possible groups aut b and the configurations of singular fibers for which each group occurs

configurations of kodaira fibers on rational elliptic surfaces i n t r o d u c t i o n l legend 6 the list 7 i d i s c r i m i n a n t cons ide ra t i ons 14 if po l a r s of p lane curves 16 ili in t r ins ic g e o m e t r y on g e n u s two curves 19 iv ell iptic qua r t i c s 25 v r a t i o n a l qua r t i c s 30 the reduc ib le case 43 to r s ion g r o u p s of ra t iona l elliptic surfaces 43 epi logue 46 references 46

conductor and capacitary inequalities for functions on topological spaces and their applications to sobolev type imbeddings in 1972 the author proved the so called conductor and capacitary inequalities for the dirichlet type integrals of a function on a euclidean domain both were used to derive necessary and sufficient

potential theoretic nature of hardy s inequality for dirichlet forms we prove that the hardy inequality for dirichlet forms of symmetric markov processes recently proved by p j fitzsimmons can be established within the framework of our potential inequality this clearly emphasizes the role played by the maximum principle in the inequality

on comparability of integral forms we prove comparability of certain homogeneous anisotropic integral forms as a consequence we obtain a hardy type inequality generalising that for the fractional laplacian we give an application to anisotropic censored stable processes in lipschitz domains

riesz decompositions in markov process theory riesz decompositions of excessive measures and excessive functions are obtained by probabilistic methods without regularity assumptions the decomposition of excessive measures is given for borel right processes the results for excessive functions are formulated within the framework of weak duality these results extend and generalize the pioneering work of hunt in this area

boundary hemivariational inequality of parabolic type abstract in this paper we consider a parabolic hemivariational inequality with a nonmonotone multivalued boundary condition and with a time dependent pseudomonotone operator we establish the existence of solutions for such inequality our proof is based on a known surjectivity result for operators of pseudomonotone type we present an example of semipermeability heat conduction problem to which the result applies

neron models lie algebras and reduction of curves of genus one let k be a discrete valuation field let ok denote the ring of integers of k and let k be the residue field of ok of characteristic p 0 let s specok let x k be a smooth geometrically connected projective curve of genus 1 over k denote by ek the jacobian of x k let x s and e s be the minimal regular models of x k and ek respectively in this article we investigate the possible relationships between the special fibers xk and ek in doing so we are led to study the geometry of the picard functor pic x s when x s is not necessarily cohomologically flat as an application of this study we are able to prove in full generality a theorem of gordon on the equivalence between the artin tate and birch swinnertondyer conjectures recall that when k is algebraically closed the special fibers of elliptic curves are classified according to their kodaira type which is denoted by a symbol t in i n n z 0 ii ii iii iii iv iv given a type t and a positive integer m we denote by mt the new type obtained from t by multiplying all the multiplicities of t by m when k is algebraically closed the relationships between the type of a curve of genus 1 and the type of its jacobian can be summarized as follows

pointwise estimates for the ground state of singular dirichlet fractional laplacian we establish sharp pointwise estimates for the ground states of some singular fractional laplace operators on relatively compact euclidean subsets the considered operators are of the type where is the fractional laplacian on an open subset of with zero exterior condition and the intrinsic ultracontractivity property for such an operators is discussed as well and a sharp large time asymptotic for their heat kernels is derived

conductor inequalities and criteria for sobolev type two weight imbeddings a typical inequality handled in this article connects the lp norm of the gradient of a function to a one dimensional integral of the p capacitance of the conductor between two level surfaces of the same function such conductor inequalities lead to necessary and sufficient conditions for multi dimensional and one dimensional sobolev type inequalities involving two arbitrary measures compactness criteria and two sided estimates for the essential norm of the related imbedding operator are obtained some counterexamples are presented to illustrate the peculiarities arising in the case of higher derivatives criteria for two weight inequalities with fractional sobolev norms of order l 2 are found

strong continuity of generalized feynman kac semigroups necessary and sufficient conditions let e d e be a strongly local quasi regular symmetric dirichlet form on l2 e m and xt t 0 px x e the diffusion process associated with e d e for u d e e u has a quasi continuous version u and u xt has fukushima s decomposition u xt u x0 mtu ntu where mtu is the martingale part and ntu is the zero energy part in this paper we study the strong continuity of the generalized feynman kac semigroup defined by ptuf x ex entuf xt t 0 two necessary and sufficient conditions for ptu t 0 to be strongly continuous are obtained by considering the quadratic form qu d e b where qu f f e f f e u f2 for f d e b and the energy measure u of u respectively an example is also given to show that ptu t 0 is strongly continuous when u is not a measure of the kato class but of the hardy class with the constant u e 12 cf definition 4 5

bielliptic curves of genus three and the torelli problem for certain elliptic surfaces abstract we study the hodge structure of elliptic surfaces which are canonically defined from bielliptic curves of genus three we prove that the period map for the second cohomology has one dimensional fibers and the period map for the total cohomology is of degree twelve and moreover by adding the information of the hodge structure of the canonical divisor we prove a generic torelli theorem for these elliptic surfaces finally we give explicit examples of the pair of non isomorphic elliptic surfaces which have the same hodge structure on themselves and the same hodge structure on their canonical divisors

coercive and semicoercive hemivariational inequalities variational inequalities have a concrete mechanical meaning they are expressions of the principle of virtual work or power in its inequality form in the case of lack of monotonicity of the underlying stress strain or reaction displacement conditions or equivalently if the corresponding energy functionals are nonconvex the variational expressions are no longer variational inequalities another type of inequality expression arises as variational formulation of the problem these expressions have been introduced in mechanics by the author and are called hemivariational inequalities the aim of this paper is the formulation of an abstract mathematical theory for coercive and semicoercive hemivariational inequalities

effective invariants of braid monodromy in this paper we construct new invariants of algebraic curves based on not necessarily generic braid monodromies such invariants are effective in the sense that their computation allows for the study of zariski pairs of plane curves moreover the zariski pairs found in this work correspond to curves having conjugate equations in a number field and hence are not distinguishable by means of computing algebraic coverings we prove that the embeddings of the curves in the plane are not homeomorphic we also apply these results to the classification problem of elliptic surfaces

boundary hemivariational inequality problems with doubly nonlinear operators in this paper we investigate a class of nonlinear boundary hemivariational inequality problems under suitable hypotheses the existence of solutions is established via rewriting these problems into a class of evolution inclusions and using the discretization method and the theory of pseudomonotone operators moreover the continuous dependence result of the solutions to the initial data is given

a system of evolution hemivariational inequalities modeling thermoviscoelastic frictional contact abstract in this paper we prove the existence and uniqueness of the weak solution for a dynamic thermoviscoelastic problem which describes frictional contact between a body and a foundation we employ the kelvin voigt viscoelastic law include the thermal effects and consider the general nonmonotone and multivalued subdifferential boundary conditions the model consists of the system of the hemivariational inequality of hyperbolic type for the displacement and the parabolic hemivariational inequality for the temperature the existence of solutions is proved by using a surjectivity result for operators of pseudomonotone type the uniqueness is obtained for a large class of operators of subdifferential type satisfying a relaxed monotonicity condition

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

the cone conjecture for calabi yau pairs in dimension 2 a central idea of minimal model theory as formulated by mori is to study algebraic varieties using convex geometry the cone of curves of a projective variety is defined as the convex cone spanned by the numerical equivalence classes of algebraic curves the dual cone is the cone of nef line bundles for fano varieties varieties with ample anticanonical bundle these cones are rational polyhedral by the cone theorem 21 theorem 3 7 for more general varieties these cones are not well understood they can have infinitely many isolated extremal rays or they can be round both phenomena occur among calabi yau varieties such as k3 surfaces 22 which can be considered the next simplest varieties after fano varieties the morrison kawamata cone conjecture would give a clear picture of the nef cone for calabi yau varieties 29 30 19 the conjecture says that the action of the automorphism group of the variety on the nef cone has a rational polyhedral fundamental domain the conjecture includes an analogous statement about the movable cone see section 2 for details thus for calabi yau varieties the failure of the nef cone to be rational polyhedral is always explained by an infinite discrete group of automorphisms of the variety it is not clear where these automorphisms should come from nonetheless the conjecture has been proved for calabi yau surfaces by sterk looijenga and namikawa 41 33 19 the heart of the proof being the torelli theorem for k3 surfaces of piatetski shapiro and shafarevich 3 theorem 11 1 kawamata proved the cone conjecture for all 3 dimensional calabi yau fiber spaces over a positive dimensional base 19 the conjecture is wide open for calabiyau 3 folds despite significant results by oguiso and peternell 38 szendroi 43 uehara 46 and wilson 48 the conjecture was generalized from calabi yau varieties to klt calabi yau pairs x in 45 here is a divisor on x and calabi yau means that kx rather than kx is numerically trivial in this paper we prove the cone conjecture for all klt calabi yau pairs of dimension 2 theorem 4 1 using the geometry of groups acting on convex cones and reduction to the case of k3 surfaces this is enough to show that the conjecture is reasonable in the greater generality of pairs more concretely the theorem gives control over the nef cone and the automorphism group for a large class of rational surfaces including the fano surfaces as well as many others in particular we get a good description of when the cox ring or total coordinate ring is finitely generated in this class of surfaces corollary 5 1 thanks to caucher birkar igor dolgachev brian harbourne artie prendergastsmith chenyang xu and the referees for their comments

on existence of solutions for parabolic hemivariational inequalities abstract a class of parabolic hemivariational inequalities is considered in which the energy function is locally lipschitz not necessarily convex or differentiable and the nonlinear evolution operator is multivalued and generalized pseudomonotone using techniques of multivalued analysis and a surjectivity result for l generalized pseudomonotone operators we prove the existence for a cauchy problem and a periodic problem some applications to nonsmooth mechanics are also indicated

exceptional curves on rational numerically elliptic surfaces a numerically elliptic surface is a complete smooth algebraic surface x over an algebraically closed field k with a proper morphism f x c to a smooth curve c such that the general fiber off is an integral curve of arithmetic genus 1 if the generic fiber is smooth the surface is called elliptic otherwise it is called quasi elliptic the latter only can occur if k has characteristic 2 or 3 in which case the general fiber is a rational curve with an ordinary cusp bm if no fiber off contains an exceptional cwue i e a smooth irreducible curve isomorphic to fp and having self intersection l then x is said to be minimal all elliptic surfaces will hereafter be assumed to be minimal one says that an elliptic surface x is jacobian if the smooth points of the generic fiber x comprise the jacobian curve of x it is equivalent for x to have a rational point or for f to have a section for a rational jacobian numerically elliptic surface the exceptional curves are precisely the sections of the libration which provides a tool by which an enumeration of the exceptional curves on a rational jacobian numerically elliptic surface can be carried out cf mp hl mop whether jacobian or not a rational

hardy s inequality for dirichlet forms abstract we prove an abstract form of hardy s l2 inequality in which the dirichlet integral is replaced by the dirichlet form of a general symmetric markov process a number of examples are provided

non symmetric perturbations of symmetric dirichlet forms abstract we provide a path space integral representation of the semigroup associated with the quadratic form obtained by lower order perturbation of a symmetric local dirichlet form the representation is a combination of feynman kac and girsanov formulas and extends previously known results in the framework of symmetric diffusion processes through the use of the hardy class of smooth measures which contains the kato class of smooth measures

regularity and rothe method error estimates for parabolic hemivariational inequality this paper deals with regularity of solutions to the abstract operator version of parabolic partial differential inclusion of the form u t au t j u t f t with the multivalued term given in the form of clarke subdifferential of a locally lipschitz functional j using the rothe method it is shown that under appropriate assumptions on the data the solution has the increased regularity three regularity theorems are given the first one concerns the regularity of solution in the besov space b2 1 2 0 t h the second theorem provides assumption under which the solution lies in the space h1 0 t h l 0 t v c 0 t vweak the last one shows that if the operator a is strongly monotone and the multivalued term satisfies the relaxed monotonicity assumption then the unique solution also belongs to h1 0 t v w1 0 t h in the last case the error estimates on the rothe method are also proved

a note on an inequality involving the normal distribution the following inequality is useful in studying a variation of the classical isoperimetric problem let x be normally distributed with mean 0 and variance 1 if g is absolutely continuous and g x has finite variance then e lbrack g x rbrack 2 geq operatorname var lbrack g x rbrack with equality if and only if g x is linear in x the proof involves expanding g x in hermite polynomials

surfaces of globally f regular and f split type we prove that normal projective surfaces of dense globally f split type respectively globally f regular type are of calabi yau type respectively fano type

automorphisms of finite order on gorenstein del pezzo surfaces in this paper we shall determine all actions of groups of prime order p with p 5 on gorenstein del pezzo singular surfaces y of picard number 1 we show that every order p element in aut y aut y y being the minimal resolution of y is lifted from a projective transformation of p 2 we also determine when aut y is finite in terms of k 2 y sing y and the number of singular members in k in particular we show that either aut y 2 a 3 b for some 1 5 there is at least one element gp of order p in aut y hence aut y is infinite

on the potential theory of symmetric markov processes on reprend des resultats de dynkin et on considere un processus de markov fort symetrique continu a droite on etudie la relation existant entre le cone de mesures positives d energie finie et la capacite

rational surfaces having only a finite number of exceptional curves we characterize the rational surfaces x which have a finite number of 1 curves under the assumption that kx is nef and having self intersection zero

nonlocal operators of order near zero abstract we study dirichlet forms defined by nonintegrable levy kernels whose singularity at the origin can be weaker than that of any fractional laplacian we show some properties of the associated sobolev type spaces in a bounded domain such as symmetrization estimates hardy inequalities compact inclusion in l 2 or the inclusion in some lorentz space we then apply those properties to study the associated nonlocal operator l and the dirichlet and neumann problems related to the equations l u f x and l u f u in

a coherent analysis of stokes flows under boundary conditions of friction type this paper is concerned with the stationary and nonstationary flow of viscous incompressible fluid under boundary conditions of friction type which are certain nonlinear boundary conditions similar to the so called signorini boundary condition in elasticity we assume that the flow is governed by the linear stokes equation while the boundary condition is nonlinear from the methodological viewpoint the analysis is carried out in a coherent way starting from study of the related boundary value problems for the stationary flow by means of the theory of variational inequalities and getting to wellposedness of the initial boundary value problems for the nonstationary flow by means of the nonlinear semigroup theory from the viewpoint of applications we mention original motivations and include some new generalizations like the cases of anisotropic friction and inhomogeneous boundary value

dynamic hemivariational inequalities in contact mechanics abstract this paper gives a review of results on the existence and uniqueness of solutions to some mechanical contact problems the second order evolution problems with a general normal compliance response condition and a normal damped response one in viscoelasticity are discussed finally a new result for a problem which includes the slip displacement dependent friction and the tresca model is provided

hemivariational inequalities for stationary navier stokes equations in this paper we study a class of inequality problems for the stationary navier stokes type operators related to the model of motion of a viscous incompressible fluid in a bounded domain the equations are nonlinear navier stokes ones for the velocity and pressure with nonstandard boundary conditions we assume the nonslip boundary condition together with a clarke subdifferential relation between the pressure and the normal components of the velocity the existence and uniqueness of weak solutions to the model are proved by using a surjectivity result for pseudomonotone maps we also establish a result on the dependence of the solution set with respect to a locally lipschitz superpotential appearing in the boundary condition

rothe method for parabolic variational hemivariational inequalities abstract the paper deals with the convergence analysis of the semidiscrete rothe scheme for the parabolic variational hemivariational inequality with the nonlinear pseudomonotone elliptic operator the problem involves both a discontinuous and nonmonotone multivalued term as well as a monotone term with potentials which assume infinite values and hence are not locally lipschitz we prove the existence of a solution and establish a convergence result of a numerical semidiscrete scheme the proof can be viewed both as the proof of solution existence as well as the proof of the convergence of a numerical semidiscrete scheme the numerical simulations to present the rate of convergence with respect to space and time for piecewise linear finite elements are presented as well

automorphisms of finite order on rational surfaces with an appendix by i dolgachev abstract we classify minimal pairs x g for smooth rational projective surface x and finite group g of automorphisms on x we also determine the fixed locus x g and the quotient surface y x g as well as the fundamental group of the smooth part of y the realization of each pair is included mori s extremal ray theory and recent results of alexeev and also ambro on the existence of good anti canonical divisors are used

multiple fibers on rational elliptic surfaces our main result theorem 0 1 classifies multiple fibers on rational elliptic surfaces over algebraically closed fields of arbitrary characteristic one result of this is the existence in positive characteristics of tame multiple fibers of additive type for several of the kodaira fiber types for which no examples were previously known 0 introduction we work in this paper over an algebraically closed field k of arbitrary characteristic p an elliptic surface f x b is a fibration of a complete smooth surface x over a complete smooth curve b such that the generic fiber is a smooth curve of genus one it is natural to wonder what kind of special fibers arise we answer this in the case of rational surfaces giving as a result examples of tame multiple fibers of additive type for every p o and for all such types except ib b 4 cf 5 to our knowledge the only example heretofore recognized is of multiplicity 2 and kodaira type iox due to katsura ka l1 although since our results were obtained we have seen a preprint of katsura and ueno ku giving other examples mostly for p 7 2 3 and kodaira type not ib b 0 any special fiber is an effective divisor on x and so can be written as mf menjcj where each curve cj is reduced and irreducible and the coefficients are positive integers with g c d nj 1 the positive integer m is the rnultiplicity of the fiber mf which is said to be a multiple fiber whenever m 1 the form of the divisor f enjcj is very restricted such a divisor is an indecomposable curve of canonical type mu a topological classification of all such curves has been given by kodaira ko cf 5 we refer to the classes which arise in this classification as the kodaira fiber types more generally the kodaira type of the fiber mf is mt where t is the type of f over an algebraically closed field k it is known that any multiple fiber mf of multiplicity m on a surface x is of the form mt where t is a kodaira type and m is divisible by and in characteristic 0 equal to the order of the normal bundle ox f s of e pic f of f in x but the extent to which these conditions are sufficient for there to occur on some elliptic surface a multiple fiber of type mt is not known of particular interest to us here are the tame multiple fibers of additive type these being fibers mf of multiplicity m where pic f is the additive group ga of the ground field k and m equals the order in ga f ox f s of these are possible only if p the characteristic of k is positive since ga only then has ptorsion but their occurrence is poorly understood received by the editors march 21 1987 1980 mathematzcs subject classzficatzon 1985 re szon primary 14j25 14m20 14d99

steady flow of generalized newtonian fluid with multivalued rheology and nonmonotone friction law abstract we study the stationary incompressible flow of a generalized newtonian fluid described by a nonlinear multivalued maximal monotone constitutive law and a multivalued nonmonotone frictional boundary condition we provide results on the existence and uniqueness of a solution to the variational form of the problem when the multivalued laws are of a subdifferential form we prove the existence of a solution to a variational hemivariational inequality for the flow s velocity field

boundary control problems with nonlinear state equation first order necessary conditions of optimality are obtained for boundary control problems governed by parabolic equations with nonlinear boundary value conditions

quadratic forms corresponding to the generalized schrodinger semigroups suppose that xt is the standard brownian motion in rd d 3 that h1 rd is a bounded continuous function such that 2 belongs to the kato class and is a measure belonging to the kato class let a t be defined as a t xt x0 t0 xs dxs and let a t be the continuous additive functional with as its revuz measure define at as the sum of the two additive functionals above then the semigroup defined as ttf x ex eatf xt is called a generalized schrodinger semigroup in this paper we identify the quadratic form corresponding to tt as e h1 rd with e u v 12 u x v x dx rd uv x x dx rdu x v x dx