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Displaying 61 –
80 of
615
We show, using a direct variational approach, that the second boundary value problem for the Monge-Ampère equation in with exponential non-linearity and target a convex body is solvable iff is the barycenter of Combined with some toric geometry this confirms, in particular, the (generalized) Yau-Tian-Donaldson conjecture for toric log Fano varieties saying that admits a (singular) Kähler-Einstein metric iff it is K-stable in the algebro-geometric sense. We thus obtain a new proof and...
Optimal control problems for semilinear elliptic equations
with control constraints and pointwise state constraints are
studied. Several theoretical results are derived, which are
necessary to carry out a numerical analysis for this class of
control problems. In particular, sufficient second-order optimality
conditions, some new regularity results on optimal controls and a
sufficient condition for the uniqueness of the Lagrange multiplier
associated with the state constraints are presented.
Gaseous detonation is a phenomenon with very complicated dynamics which
has been studied extensively by physicists, mathematicians and engineers for many years.
Despite many efforts the problem is far from a complete resolution. Recently the theory
of subsonic detonation that occurs in highly resistant porous media was proposed in [4].
This theory provides a model which is realistic, rich and suitable for a mathematical study.
In particular, the model is capable of describing the transition from...
We report on new results concerning the global well-posedness, dissipativity and attractors for the quintic wave equations in bounded domains of with damping terms of the form , where or . The main ingredient of the work is the hidden extra regularity of solutions that does not follow from energy estimates. Due to the extra regularity of solutions existence of a smooth attractor then follows from the smoothing property when . For existence of smooth attractors is more complicated and follows...
In this paper we will give a brief survey of recent regularity results for Fourier integral operators with complex phases. This will include the case of real phase functions. Applications include hyperbolic partial differential equations as well as non-hyperbolic classes of equations. An application to an oblique derivative problem is also given.
We give a survey of results on the Lieb-Thirring inequalities for the eigenvalue moments of Schrödinger operators. In particular, we discuss the optimal values of the constants therein for higher dimensions. We elaborate on certain generalisations and some open problems as well.
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