Exhaustive measures in arbitrary topological vector spaces
Exhaustivity in Topological Riesz Spaces with the Principal Projection Property
Exhaustive and uniformly exhaustive elements are studied in the setting of locally solid topological Riesz spaces with the principal projection property. We study the structure of the order interval [0,x] when x is an exhaustive element and the structure of the solid hull of a set of uniformly exhaustive elements.
Existence and analyticity of a parabolic evolution operator for nonautonomous linear equations in Banach spaces.
Existence and integral representation of regular extensions of measures
Let ℒ be a δ-lattice in a set X, and let ν be a measure on a sub-σ-algebra of σ(ℒ). It is shown that ν extends to an ℒ-regular measure on σ(ℒ) provided ν*|ℒ is σ-smooth at ∅ and ν*(L) = inf ν*(U)|X ∖ U ∈ ℒ, Usupset L for all L ∈ ℒ. Moreover, a Choquet type representation theorem is proved for the set of all such extensions.
Existence and nonexistence results for a class of linear and semilinear parabolic equations related to some Caffarelli-Kohn-Nirenberg inequalities
In this work we study the problem in , in , on , in , is a bounded regular domain such that , , , , and are positive functions such...
Existence and nonexistence results for anisotropic quasilinear elliptic equations
Existence and regularity of minima for integral functionals noncoercive in the energy space
Existence and stability of measure differential equations
Existence and uniqueness results for solutions of nonlinear equations with right hand side in
We prove an existence and uniqueness theorem for the elliptic Dirichlet problem for the equation div a(x,∇u) = f in a planar domain Ω. Here and the solution belongs to the so-called grand Sobolev space . This is the proper space when the right hand side is assumed to be only -integrable. In particular, we obtain the exponential integrability of the solution, which in the linear case was previously proved by Brezis-Merle and Chanillo-Li.
Existence et prolongement des solutions holomorphes des équations aux dérivées partielles
Existence for elliptic equations in having lower order terms with natural growth.
Existence of a multiplicative functional and joint spectra
Existence of bases and the dual splitting relation for Fréchet spaces
Existence of best approximations
Existence of Borel lifting
Existence of bounded solutions for nonlinear degenerate elliptic equations in Orlicz spaces.
Existence of critical points for some noncoercive functionals
Existence of entropy solutions for some nonlinear problems in Orlicz spaces.
Existence of infinite-dimensional Lie algebra for a unitary group on a Hilbert space and related aspects
We show that for any strongly closed subgroup of a unitary group of a finite von Neumann algebra, there exists a canonical Lie algebra which is complete with respect to the strong resolvent topology. Our analysis is based on the comparison between measure topology induced by the tracial state and the strong resolvent topology we define on the particular space of closed operators on the Hilbert space. This is an expository article of the paper by both authors in Hokkaido Math. J. 41 (2012), 31-99,...
Existence of open quasiconvex subsets dense in a given space