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Volume growth, ?a priori? estimates, and geometric applications
Geometric And Functional Analysis, 2003Let \((M,\langle\;,\;\rangle)\) be a smooth, connected, non-compact, complete Riemannian manifold of dimension \(m\geq 2\), \(\nabla\) (resp. div) the gradient (resp. divergence) operator, \(| \;| \) the norm corresponding to \(\langle\;,\;\rangle\) and the \(\varphi\)-Laplacian \(L_\varphi\) defined, for \(u\in C^1(M)\), by \(L_\varphi (u) := \text ...
PIGOLA, STEFANO +2 more
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Weak Solutions, A Priori Estimates
2017The fundamental laws of continuum mechanics that can be interpreted as infinite families of integral identities equivalent to systems of partial differential equations give rise to the concept of weak (or variational) solutions that can be vastly extended to extremely divers physical systems of various sorts.
Eduard Feireisl, Antonín Novotný
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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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