On the behaviour of solutions to the nonlinear elliptic Neumann problem in unbounded domains
The asymptotic behaviour is studied for minima of regular variational problems with Neumann boundary conditions on noncompact part of boundary.
On the behaviour of the solutions to p-Laplacian equations as p goes to 1
On the Bethe-Sommerfeld conjecture
We consider the operator in , of the form with a function periodic with respect to a lattice in . We prove that the number of gaps in the spectrum of is finite if . Previously the finiteness of the number of gaps was known for . Various approaches to this problem are discussed.
On the bicubic spline collocation method for Poisson's equations.
On the Boundary Behaviour of the Perron Generalized Solution.
On the Boundary Element Method for Some Nonlinear Boundary Value Problems.
On the boundary element method for the Signorini problem of the Laplacian.
On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions
On the boundedness of multipliers, commutators and the second derivatives of Green’s operators on and
On the Calabi-Yau equation in the Kodaira-Thurston manifold
We review some previous results about the Calabi-Yau equation on the Kodaira-Thurston manifold equipped with an invariant almost-Kähler structure and assuming the volume form T2-invariant. In particular, we observe that under some restrictions the problem is reduced to aMonge-Ampère equation by using the ansatz ˜~ω = Ω− dJdu + da, where u is a T2-invariant function and a is a 1-form depending on u. Furthermore, we extend our analysis to non-invariant almost-complex structures by considering some...
On the characterization of harmonic functions with initial data in Morrey space
Let be a metric measure space satisfying the doubling condition and an -Poincaré inequality. Consider the nonnegative operator generalized by a Dirichlet form on . We will show that a solution to on satisfies an -Carleson condition if and only if can be represented as the Poisson integral of the operator with the trace in the generalized Morrey space , where is a nonnegative function defined on a class of balls in . This result extends the analogous characterization founded...
On the choice of iteration parameters in the Stone incomplete factorization
The paper is concerned with the iterative solution of sparse linear algebraic systems by the Stone incomplete factorization. For the sake of clarity, the algorithm of the Stone incomplete factorization is described and, moreover, some properties of the method are derived in the paper. The conclusion is devoted to a series of numerical experiments focused on the choice of iteration parameters in the Stone method. The model problem considered showe that we can, in general, choose appropriate values...
On the coincidence set in biharmonic variational inequalities with thin obstacles
On the combined effect of boundary approximation and numerical integration on mixed finite element solution of 4th order elliptic problems with variable coefficients
On the combined effect of boundary approximation and numerical integration on mixed finite element solution of 4th order elliptic problems with variable coefficients
Error estimates for the mixed finite element solution of 4th order elliptic problems with variable coefficients, which, in the particular case of aniso-/ortho-/isotropic plate bending problems, gives a direct, simultaneous approximation to bending moment tensor field and displacement field 'u', have been developed considering the combined effect of boundary approximation and numerical integration.
On the complex structure of positive solutions to Matukuma-type equations
On the concentration of solutions of singularly perturbed Hamiltonian systems in .
On the Condition Number of Boundary Integral Operators for the Exterior Dirichlet Problem for the Helmholtz Equation.
On the Construction of Finite Difference Schemes Approximating Generalized Solutions
On the Construction of Optimal Mixed Finite Element Methods for the Linear Elasticity Problem.