the bar partial neumann problem on product domains in mathbb c n let omega omega 1 times cdots times omega n subset mathbb c n where omega j subset mathbb c is a bounded domain with smooth boundary we study the solution operator to the overline partial neumann problem for 0 1 forms on in particular we construct singular functions which describe the singular behavior of the solution as a corollary our results carry over to the overline partial neumann problem for 0 q forms despite the singularities we show that the canonical solution to the overline partial equation obtained from the neumann operator does not exhibit singularities when given smooth data

a smooth variational principle with applications to hamilton jacobi equations in infinite dimensions abstract we prove that if x is a banach space which admits a smooth lipschitzian bump function then for every lower semicontinuous bounded below function there exists a lipschitzian smooth function g on x such that f g attains its strong minimum on x thus extending a result of borwein and preiss we then show how the above result can be used to obtain existence and uniqueness results of viscosity solutions of hamilton jacobi equations in infinite dimensional banach spaces a without assuming the radon nikodym property

on smooth variational principles in banach spaces abstract a new smooth variational principle for spaces admitting frechet differentiable bump functions is proved further it is shown that each proper lower semicontinuous bounded below function can be supported by a smooth function with locally holder derivative if and only if the space is superreflexive some geometrical refinements of the borwein preiss smooth variational principle using deville s techniques are obtained

on the equivalence of some basic principles in variational analysis the primary goal of this paper is to study relationships between certain basic principles of variational analysis and its applications to nonsmooth calculus and optimization considering a broad class of banach spaces admitting smooth renorms with respect to some bornology we establish an equivalence between useful versions of a smooth variational principle for lower semicontinuous functions an extremal principle for nonconvex sets and an enhanced fuzzy sum rule formulated in terms of viscosity normals and subgradients with controlled ranks further refinements of the equivalence result are obtained in the case of a frechet differentiable norm based on the new enhanced sum rule we provide a simplified proof for the refined sequential description of approximate normals and subgradients in smooth spaces

partially smooth variational principles and applications we discuss a smooth variational principle for partially smooth viscosity subdifferentials and explore its applications in nonsmooth analysis

construction of coupling coefficients of su 4 in a supermultiplet basis matrix elements of the unit tensor operators of ranks 1 2 and 1 1 in the non orthonormal draayer basis of su 4 are found the evaluation algorithms for the su 4 coupling coefficients are proposed for coupling one arbitrary and one four six or ten dimensional irreducible representation of su 4 in the su 2 su 2 chain as well as in the case of the semistretched coupling the construction of the overlaps of the draayer basis states is considered

a smooth variational principle with applications to subdifferentiability and to differentiability of convex functions we show that typically lower semicontinuous functions on a banach space densely inherit lower subderivatives of the same degree of smoothness as the norm in particular every continuous convex function on a space with a g teaux weak hadamard frechet smooth renorm is densely g teaux weak hadamard frechet differentiable our technique relies on a more powerful analogue of ekeland s variational principle in which the function is perturbed by a quadratic like function this smooth variational principle has very broad applicability in problems of nonsmooth analysis

a generalization of ekeland s ϵ variational principle and its borwein preiss smooth variant abstract we give a generalization of ekeland s variational principle and of its borwein preiss smooth variant replacing the distance and the norm by a gauge type lower semi continuous function as an application of this generalization we show that if on a banach space x there exists a lipschitz smooth bump function then every continuous convex function on an open subset u of x is densely differentiable in u this generalizes the borwein preiss theorem on the differentiability of convex functions

necessary suboptimality and optimality conditions via variational principles the paper aims to develop some basic principles and tools of nonconvex variational analysis with applications to necessary suboptimality and optimality conditions for constrained optimization problems in infinite dimensions we establish a certain subdifferential variational principle as a new characterization of asplund spaces this result is different from conventional support forms of variational principles and appears to be convenient for applications to nonsmooth optimization based on the subdifferential variational principle we obtain new necessary conditions for suboptimal solutions in general nonsmooth optimization problems with equality inequality and set constraints in asplund spaces in this way we establish the so called sequential normal compactness properties of constraint sets that play an essential role in infinite dimensional variational analysis and its applications as a by product of our approach we derive various forms of necessary optimality conditions for nonsmooth constrained problems in infinite dimensions which extend known results in that direction

sobolev estimates for the bar partial neumann operator on domains inc n admitting a defining function that is plurisubharmonic on the boundary neumann operator on domains inc n admitting a defining function that is plurisubharmonic on the boundary

localization of the kobayashi metric and the boundary continuity of proper holomorphic mappings a classical theorem of carath6odory 8 states that every biholomorphic map f d d2 between domains in the complex plane c bounded by simple closed jordan curves extends to a homeomorphism of 31 onto 2 there are some well known generalizations of this result to domains in ie a if d t and d2 are bounded pseudoconvex domains in 112 with if2 boundary and if the infinitezimal kobayashi metric on d2 grows sufficiently fast near the boundary of d2 ko2 g x xl d z bdz for some e e 0 1 then every proper holomorphic map f dt d2 extends to a h61der continuous map of 51 onto 32 2 3 10 25 29 32 this holds in particular if 92 is strictly pseudoconvex or if it is pseudoconvex with real analytic boundary the same result holds if d2 is only piecewise smooth strongly pseudoconvex 31 further results treat exceptional cases such as the balls 1 reinhardt domains 5 24 domains with many symmetries 4 and analytically bounded hartogs domains in c 2 i1 biholomorphic maps between certain types of nonpseudoconvex domains with real analytic boundaries were treated in 13 and 27 besides the papers mentioned above there is a vast literature concerning smooth extension of proper holomorphic maps of smoothly bounded pseudoconvex domains 6 7 12 14 to mention just a few in the present paper we obtain some results on the continuous extension of proper holomorphic maps f d1 2 under local assumptions on the boundaries bd1 and bd2 one of the main results is

some new results on stability of ekeland s ϵ variational principle abstract in this paper we give an example and point out that solutions of ekeland s variational principle are not always lower semicontinuous in infinite dimensional banach spaces even with respect to the uniform metric further the example shows that the solutions need not be almost lower semicontinuous when the convergence of sequence of functions is weakened to painleve kuratowski epigraphical convergence to provide some results of stability we prove the almost lower semicontinuity of solutions in a general framework

the cauchy riemann equations on product domains we establish the l 2 theory for the cauchy riemann equations on product domains provided that the cauchy riemann operator has closed range on each factor we deduce regularity of the canonical solution on p 1 forms in special sobolev spaces represented as tensor products of sobolev spaces on the factors of the product this leads to regularity results for smooth data