An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. Part III : Petrov type III space-times
An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. — Part II : Petrov type D space-times
An explicit formula for symmetric polynomials related to the eigenfunctions of Calogero-Sutherland models.
An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection
We describe a numerical method for the equation in with Dirichlet boundary and initial conditions which is a combination of the method of characteristics and the finite-difference method. We prove both an a priori local error-estimate of a high order and stability. Example 3.3 indicates that our approximate solutions are disturbed only by a minimal amount of the artificial diffusion.
An explicit potential theory for the stokes resolvent boundary value problems in three dimensions.
An explicit right inverse of the divergence operator which is continuous in weighted norms
The existence of a continuous right inverse of the divergence operator in , 1 < p < ∞, is a well known result which is basic in the analysis of the Stokes equations. The object of this paper is to show that the continuity also holds for some weighted norms. Our results are valid for Ω ⊂ ℝⁿ a bounded domain which is star-shaped with respect to a ball B ⊂ Ω. The continuity results are obtained by using an explicit solution of the divergence equation and the classical theory of singular integrals...
An explicit separate solution for the Tzitzeica equation.
An explicit solution of coupled viscous Burgers' equation by the decomposition method.
An explicit solution to a system of implicit differential equations
An exponential transform and regularity of free boundaries in two dimensions
An extension of a multiplicity theorem by Ricceri with an application to a class of quasilinear equations
A recent multiplicity result by Ricceri, stated for equations in Hilbert spaces, is extended to a wider class of Banach spaces. Applications to nonlinear boundary value problems involving the p-Laplacian are presented.
An extension of Rothe's method to non-cylindrical domains
In this paper Rothe’s classical method is extended so that it can be used to solve some linear parabolic boundary value problems in non-cylindrical domains. The corresponding existence and uniqueness theorems are proved and some further results and generalizations are discussed and applied.
An Extension of the Lax-Richtmyer Theory.
An extension theorem for supertemperatures.
An Extrerior Mixed Boundary Value Problem for the Helmholtz Equation
An -Galerkin method for a Stefan problem with a quasilinear parabolic equation in nondivergence form.
An Hadamard maximum principle for the biplacian on hyperbolic manifolds
We prove the existence of a maximum principle for operators of the type , for weights with subharmonic. It is associated with certain simply connected subdomains that are produced by a Hele-Shaw flow emanating from a given point in the domain. For constant weight, these are the circular disks in the domain. The principle is equivalent to the following statement. THEOREM. Suppose is logarithmically subharmonic on the unit disk, and that the weight times area measure is a reproducing measure...
An Iff solvability condition for the oblique derivative problem
An ill posed Cauchy problem for a hyperbolic system in two space dimensions
An ill-posed nonlocal two-point problem for systems of partial differential equations.