Boundary regularity

In this paper, we prove global second derivative estimates for solutions of the Dirichlet problem for the Monge-Amp`re equation when the inhomogee neous term is only assumed to be H¨lder continuous. As a consequence of our o approach, we also establish the existence and uniqueness of globally smooth solutions to the second boundary value problem for the affine maximal surface equation and affine mean curvature equation.

38p dontetvui 17-01-2013 48 8   Download

Annals of Mathematics We study the motion of an incompressible perfect liquid body in vacuum. This can be thought of as a model for the motion of the ocean or a star. The free surface moves with the velocity of the liquid and the pressure vanishes on the free surface. This leads to a free boundary problem for Euler’s equations, where the regularity of the boundary enters to highest order. We prove local existence in Sobolev spaces assuming a “physical condition”, related to the fact that the pressure of a fluid has to be positive. ...

87p noel_noel 17-01-2013 68 7   Download

In this paper we study Lipschitz solutions of partial differential relations of the form (1) ∇u(x) ∈ K a.e. in Ω, where u is a (Lipschitz) mapping of an open set Ω ⊂ Rn into Rm , ∇u(x) is its gradient (i.e. the matrix ∂ui (x)/∂xj , 1 ≤ i ≤ m, 1 ≤ j ≤ n, defined for almost every x ∈ Ω), and K is a subset of the set M m×n of all real m × n matrices. In addition to relation (1), boundary conditions and other conditions on u will also be considered. Relation (1)...

29p tuanloccuoi 04-01-2013 53 9   Download

MAXIMAL REGULAR BOUNDARY VALUE PROBLEMS IN BANACH-VALUED WEIGHTED SPACE RAVI P. AGARWAL, MARTIN BOHNER, AND VELI B. SHAKHMUROV Received 10 July 2004 This study focuses on nonlocal boundary value problems for elliptic ordinary and partial differential-operator equations of arbitrary order, defined in Banach-valued function spaces. The region considered here has a varying bound and depends on a certain parameter.

34p sting12 10-03-2012 38 5   Download

BOUNDARY VALUE PROBLEMS FOR THE 2ND-ORDER SEIBERG-WITTEN EQUATIONS CELSO MELCHIADES DORIA Received 8 June 2004 It is shown that the nonhomogeneous Dirichlet and Neuman problems for the 2nd-order Seiberg-Witten equation on a compact 4-manifold X admit a regular solution once the nonhomogeneous Palais-Smale condition is satisfied. The approach consists in applying the elliptic techniques to the variational setting of the Seiberg-Witten equation. The gauge invariance of the functional allows to restrict the problem to the Coulomb subspace C of configuration space.

19p sting12 10-03-2012 42 5   Download

MULTIDIMENSIONAL KOLMOGOROV-PETROVSKY TEST FOR THE BOUNDARY REGULARITY AND IRREGULARITY OF SOLUTIONS TO THE HEAT EQUATION UGUR G. ABDULLA Received 25 August 2004 Dedicated to I. G. Petrovsky This paper establishes necessary and sufficient condition for the regularity of a characteristic top boundary point of an arbitrary open subset of RN+1 (N ≥ 2) for the diffusion (or heat) equation. The result implies asymptotic probability law for the standard Ndimensional Brownian motion. 1. Introduction and main result Consider the domain Ωδ = (x,t) ∈ RN+1 : |x| 0, N ≥ 2, x = (x1 ,...

19p sting12 10-03-2012 44 5   Download

ON WEAK SOLUTIONS OF THE EQUATIONS OF MOTION OF A VISCOELASTIC MEDIUM WITH VARIABLE BOUNDARY V. G. ZVYAGIN AND V. P. ORLOV Received 2 September 2005 The regularized system of equations for one model of a viscoelastic medium with memory along trajectories of the field of velocities is under consideration. The case of a changing domain is studied. We investigate the weak solvability of an initial boundary value problem for this system. 1. Introduction The purpose of the present paper is an extension of the result of [21] on the case of a changing domain. Let Ωt ∈ Rn , 2 ≤...

31p sting12 10-03-2012 43 6   Download

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: BOUNDARY REGULARITY OF WEAK SOLUTIONS TO NONLINEAR ELLIPTIC OBSTACLE PROBLEMS

15p dauphong18 09-03-2012 34 2   Download