Elliptic boundary value problem on non-compact G-manifolds

On a Nonlinear Elliptic Boundary Value Problem

Consider a bounded domain G C R (_N>1) with smooth boundary T . Let L be a uniformly elliptic linear differential operator. Let y and ß be two maximal monotone mappings in R. We prove that, when y ? 2 satisfies a certain growth condition, given f £ L (G ) there is u € H (G) such that Lu + y(u) 3 f a.e. on G, and -du/d v e ß(u\ ) a.e. on T, where du/civ is the conormal derivative associated with...

The Monge problem on non-compact manifolds

In this paper we prove the existence of an optimal transport map on non-compact manifolds for a large class of cost functions that includes the case c(x, y) = d(x, y), under the only hypothesis that the source measure is absolutely continuous with respect to the volume measure. In particular, we assume compactness neither of the support of the source measure nor of that of the target measure.

NON-POLYNOMIAL QUARTIC SPLINE SOLUTION OF BOUNDARY-VALUE PROBLEM

Quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. Using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. Convergence analysis of sixth order method has been given. The methods are illustrated by some examples, to verify the or...

On an Eighth Order Overdetermined Elliptic Boundary Value Problem

We consider the overdetermined boundary value problem for the 4-harmonic operator, Δ4 = Δ(Δ3) , and show that if the solution of the problem exists, then the domain must be an open N -ball (N 2) . As a consequence of overdetermined problems mean value results are obtained for harmonic, biharmonic, triharmonic and 4-harmonic functions. Mathematics subject classification (2010): 35J25, 35P15, 35B50.

Spectral Theory of Elliptic Operatorson Non { Compact Manifolds