A. Vagov, 2 H. Schomerus, and V. V. Zalipaev 4 Institut für Theoretische Physik III, Bayreuth Universität, Bayreuth 95440, Germany Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom Steklov Mathematical Institute, Fontanka 27, St.-Petersburg 191023, Russia 4 Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom (Dated: July 9...

In this paper we study the regularity properties of a free boundary problem arising in the optimization of the best Sobolev trace constant in the immersion H(Ω) ↪→ L(∂Ω) for functions that vanish in a subset of Ω. This problem is also related to a minimization problem for Steklov eigenvalues.

We consider a differential system based on the coupling of the Navier-Stokes and Darcy equations for modeling the interaction between surface and subsurface flows. We formulate the problem as an interface equation, we analyze the associated (nonlinear) Steklov-Poincaré operators, and we prove its wellposedness.

The free field representation of the Zamolodchikov-Faddeev algebra for the chiral Gross-Neveu model is analysed in detail, and used to construct an integral representation for form factors of the model. ∗Email: [email protected], [email protected] †Correspondent fellow at Steklov Mathematical Institute, Moscow. ar X iv :1 30 5. 62 52 v1 [ he pth ] 2 7 M ay 2 01 3

We construct the Poincaré polynomials for Landau-Ginzburg orbifolds with projection operators. Using them we show that special types of dualities including Poincaré duality are realized under certain conditions. When Calabi-Yau interpretation exists, two simple formulae for Hodge numbers h and h are obtained.

We prove two kinds of fibering theorems for maps X → P , where X and P are Poincaré spaces. The special case of P = S yields a Poincaré duality analogue of the fibering theorem of Browder and Levine.

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove ...

We use the recently found integral representation for the dressing phase in the kinematic region of the mirror theory to simplify the TBA equations for the AdS5×S mirror model. The resulting set of equations provides an efficient starting point for both analytic and numerical studies. Email: [email protected], [email protected] Correspondent fellow at Steklov Mathematical Institute, Moscow.