All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 4 Next

Displaying 61 – 80 of 614

Showing per page

Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties

Robert J. Berman, Bo Berndtsson (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

We show, using a direct variational approach, that the second boundary value problem for the Monge-Ampère equation in ℝ n with exponential non-linearity and target a convex body P is solvable iff 0 is the barycenter of P . Combined with some toric geometry this confirms, in particular, the (generalized) Yau-Tian-Donaldson conjecture for toric log Fano varieties ( X , Δ ) saying that ( X , Δ ) admits a (singular) Kähler-Einstein metric iff it is K-stable in the algebro-geometric sense. We thus obtain a new proof and...

Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems

Eduardo Casas, Fredi Tröltzsch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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.

Recent Mathematical Results on Combustion in Hydraulically Resistant Porous Media

P. Gordon (2010)

Mathematical Modelling of Natural Phenomena

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...

Recent progress in attractors for quintic wave equations

Anton Savostianov, Sergey Zelik (2014)

Mathematica Bohemica

We report on new results concerning the global well-posedness, dissipativity and attractors for the quintic wave equations in bounded domains of ℝ 3 with damping terms of the form ( - Δ x ) θ ∂ t u , where θ = 0 or θ = 1 / 2 . 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 θ = 1 / 2 . For θ = 0 existence of smooth attractors is more complicated and follows...

Recent progress in the regularity theory of Fourier integrals with real and complex phases and solutions to partial differential equations

Michael Ruzhansky (2003)

Banach Center Publications

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.

Recent results on Lieb-Thirring inequalities

Ari Laptev, Timo Weidl (2000)

Journées équations aux dérivées partielles

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.

Currently displaying 61 – 80 of 614