Results 241 to 250 of about 717,764 (281)
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1991
This Chapter 6 and the next Chapter 7 are devoted to the proof of Theorem 1.2. In this chapter we study the operator Ap, and prove a priori estimates for the operator Ap − λI (Theorem 6.3) which will play a fundamental role in the next chapter. In the proof we make good use of Agmon’s method (Proposition 6.4). This is a technique of treating a spectral
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This Chapter 6 and the next Chapter 7 are devoted to the proof of Theorem 1.2. In this chapter we study the operator Ap, and prove a priori estimates for the operator Ap − λI (Theorem 6.3) which will play a fundamental role in the next chapter. In the proof we make good use of Agmon’s method (Proposition 6.4). This is a technique of treating a spectral
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1982
As we have shown in § 3, if A is an arbitrary operator with a dense domain and if equation (A) is correctly solvable on R(A), i.e., if one has the estimate $$ \parallel x{\parallel _E} \leqslant k\parallel Ax{\parallel _F}\;\;(x \in D(A)) $$ (7.1) then the adjoint equation (A*) is everywhere solvable.
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As we have shown in § 3, if A is an arbitrary operator with a dense domain and if equation (A) is correctly solvable on R(A), i.e., if one has the estimate $$ \parallel x{\parallel _E} \leqslant k\parallel Ax{\parallel _F}\;\;(x \in D(A)) $$ (7.1) then the adjoint equation (A*) is everywhere solvable.
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2011
In this chapter we obtain a priori estimates for elliptic operators in bounded or unbounded domains. We will use the spaces of functions introduced in Chapter 2.
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In this chapter we obtain a priori estimates for elliptic operators in bounded or unbounded domains. We will use the spaces of functions introduced in Chapter 2.
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Estimating semantic content: An A priori approach
International Journal of Intelligent Systems, 1988We present our research into the use of the logical structure of natural language discourse to generate estimates of the quantity of semantic content contained within a passage. These estimates of the degree of meaningfulness are recovered from the logical form of the passage, without actually recovering its meaning or necessitating real understanding.
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2003
Abstract A priori estimates play a decisive role in the analysis of any nonlinear problem. They determine the class of functions, where the solutions are looked for. A priori estimates resulting from the basic physical principles — conservation (or balance) of mass, momentum, and energy — are discussed.
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Abstract A priori estimates play a decisive role in the analysis of any nonlinear problem. They determine the class of functions, where the solutions are looked for. A priori estimates resulting from the basic physical principles — conservation (or balance) of mass, momentum, and energy — are discussed.
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A Priori Wire Length Estimation
2001This chapter presents an overview of wire length estimation models. Donath’s pioneering hierarchical placement model [Don79] will be described in the second section and its resulting average wire length estimations will be evaluated.
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A priori estimates for harmonic mappings
Analysis, 2007SummaryWe give a new proof of a well known regularity result for harmonic mappings between Riemannian manifolds due to Giaquinta and Hildebrandt [3]. The proof uses a modification of a method due to L. Caffarelli [2] to show interior and boundary Hölder-continuity of harmonic mappings, whose images lie in a regular ball.
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Some a priori estimates in mechanics
Russian Physics Journal, 1992The scope for quantitative a priori estimators is considered and some of the input data are of probabilistic type subject to given constraints. Corresponding estimates are given for the stability of a rod with initial imperfections on pulsed loading, boundary-value problems for a planar potential, and topics in planar elasticity; these relate the ...
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A Priori Estimates for Prescribing Scalar Curvature Equations
The Annals of Mathematics, 1997This is a remarkable paper in the study of scalar curvature equations. There are two important contributions in this paper. One is that they use the Kelvin transform and the maximum principle to derive estimates on solutions in the region where the prescribed scalar curvature is negative.
Chen, Wenxiong, Li, Congming
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A priori weighting for parameter estimation
Journal of Inverse and Ill-posed Problems, 2008The author considers parameter estimation as an element of inverse modelling in which measurements (data) are used to infer the parameters in a mathematical model. He assumes that parameter estimation can be viewed as an optimization problem in which the objective function representing the data misfit is minimized in a given norm.
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