Necessary conditions for the multiple integral problem and elliptic variational inequalities
Cohomology Groups of Locally q-Complete Morphisms with r-Complete Base.
q-completeness and q-concavity of the union of open subspaces.
Some convexity properties of morphisms of complex spaces.
Necessary Conditions for Multiple Integral Problem in the Calculus of Variations.
Cohomology with compact supports for q-complete spaces.
Invariance of cohomological q-completeness under finite holomorphic surjections.
Holomorphic q-hulls in top degrees.
On the 2-typical de Rham-Witt complex.
Approximation theorems and homology of q-Runge domains in complex spaces.
Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative gaussian noise
The parabolic equations driven by linearly multiplicative Gaussian noise are stabilizable in probability by linear feedback controllers with support in a suitably chosen open subset of the domain. This procedure extends to Navier − Stokes equations with multiplicative noise. The exact controllability is also discussed.
Exact null internal controllability for the heat equation on unbounded convex domains
The liner parabolic equation ∂y ∂t − 1 2 Δy + F · ∇ y = 1 x1d4aa; 0 u with Neumann boundary condition on a convex open domain x1d4aa; ⊂ ℝ with smooth boundary is exactly null controllable on each finite interval if 𝒪is an open subset of x1d4aa; which contains a suitable neighbourhood of the recession cone of x1d4aa; . Here, : ℝ → ℝ is a bounded, -continuous function, and = ∇, where is convex and coercive.
The internal stabilization by noise of the linearized Navier-Stokes equation
One shows that the linearized Navier-Stokes equation in , around an unstable equilibrium solution is exponentially stabilizable in probability by an internal noise controller , , where are independent Brownian motions in a probability space and is a system of functions on with support in an arbitrary open subset . The stochastic control input is found in feedback form. One constructs also a tangential boundary noise controller which exponentially stabilizes in probability the equilibrium...
Feedback stabilization of Navier–Stokes equations
One proves that the steady-state solutions to Navier–Stokes equations with internal controllers are locally exponentially stabilizable by linear feedback controllers provided by a control problem associated with the linearized equation.
The analyticity of -concave sets of locally finite Hausdorff measure
We prove the analyticity of -concave sets of locally finite Hausdorff -measure in a -dimensional complex space. We apply it to give a removability criterion for meromorphic maps with values in -complete spaces.
Pseudoconvex domains over -complete manifolds
Differentiable distribution semi-groups
Dissipative sets and nonlinear perturbated equations in Banach spaces
The internal stabilization by noise of the linearized Navier-Stokes equation
One shows that the linearized Navier-Stokes equation in , around an unstable equilibrium solution is exponentially stabilizable in probability by an internal noise controller , , where are independent Brownian motions in a probability space and is a system of functions on with support in an arbitrary open subset . The stochastic control input is found in feedback form. One constructs also a tangential boundary noise controller which exponentially stabilizes in probability the equilibrium solution. ...
A cohomological Steinness criterion for holomorphically spreadable complex spaces
Let be a complex space of dimension , not necessarily reduced, whose cohomology groups are of finite dimension (as complex vector spaces). We show that is Stein (resp., -convex) if, and only if, is holomorphically spreadable (resp., is holomorphically spreadable at infinity). This, on the one hand, generalizes a known characterization of Stein spaces due to Siu, Laufer, and Simha and, on the other hand, it provides a new criterion for -convexity.
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