Showing papers on "A priori estimate published in 1980"
TL;DR: In this paper, the existence of classical solutions to fully non-linear second order elliptic equations with large zeroth order coefficient was proved by an a priori estimate that the C superscript 2, alpha-norm of the solution cannot lie in a certain interval of the positive real axis.
Abstract: : This report proves the existence of classical solutions to certain fully non-linear second order elliptic equations with large zeroth order coefficient. The principal tool is an a priori estimate asserting that the C superscript 2, alpha-norm of the solution cannot lie in a certain interval of the positive real axis. (Author)
9 citations
01 Jan 1980
TL;DR: In this article, it was shown that within the class of tempered solutions for suitable initial values x there is exactly one solution of {1] for which the induced point process is stationary in time.
Abstract: This model has first been studied by Lang ([1]), who was able to show the existence and uniqueness of solutions in the eauilibrium case, i. e. if one restricts oneself to those solutions X(t), for which the induced point process ( = the sequence Xi(t) , i = 1,2,..., without labelling of particles) is stationary in time. Here we show that within the class of tempered solutions for suitable initial values x there is exactly one solution of {1). Many of the ideas used in this paper go back to Lanford ([2]) and Dobrushin and Fritz ([3]), who studied an analogous system of equations in the case of deterministic NewtonJan dynamics. Our restriction to the dimension one is due to the fact that the main a priori estimate (lemma I) can only be proven in that case.
6 citations
TL;DR: In this article, a class of systems governed by second order linear parabolic partial delay-differential equations in divergence form with Cauchy conditions is considered, and the existence and uniqueness of a weak solution is proved and its a priori estimate is established.
Abstract: In this paper, a class of systems governed by second order linear parabolic partial delay-differential equations in “divergence form” with Cauchy conditions is considered. Existence and uniqueness of a weak solution is proved and its a priori estimate is established.
3 citations
01 Jun 1980
TL;DR: In this article, a priori estimate of the initial-boundary value for strictly hyperbolic systems with constant coefficients is obtained by using the technique of lambda-matrix, which assures the continuous dependence of the solution on the inhomogeneous terms of the equations.
Abstract: : This work consists of two parts. In the first, we consider initial-boundary value problems for strictly hyperbolic systems with constant coefficients: By using the technique of lambda-matrix, we obtain an a priori estimate, which assures the continuous dependence of the solution on the inhomogeneous terms of the equations. This work generalizes the former results of Majda and Osher (1975) also to the nonsymmetrical case, simplifies their proofs an removes some of their assumptions. In Part II, we develop stability theory for Burstein difference scheme approximating the above problem(m=2) with additional assumption det (A ALPHA +B2B)=0. Particularly, the problem of constructing the Kreiss symmetrizer for general multidimensional dissipative approximations is resolved, thus removing the only obstacle in developing stability theory for such approximations in the noncharacteristic case.