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On a Constrained Dirichlet Problem
SIAM Journal on Control and Optimization, 2002Summary: We consider a Dirichlet minimum problem with a pointwise constraint on the gradient, i.e., \(\| \nabla u(x)\| \leq 1\) a.e., or, equivalently, an unconstrained minimum problem with an extended-valued integrand. Since the subdifferential of this integrand is defined on the whole effective domain, the problem of the validity of the Euler ...
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1991
This chapter is devoted to studying boundary value problems for second-order elliptic equations. The variational (also known as Hilbert space) approach to the Dirichlet problem is emphasized. Maximum principles are discussed in §5.10 and §5.11, which are independent of the preceding sections and are essential reading along with §5.1, §5.2, and §5.3 ...
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This chapter is devoted to studying boundary value problems for second-order elliptic equations. The variational (also known as Hilbert space) approach to the Dirichlet problem is emphasized. Maximum principles are discussed in §5.10 and §5.11, which are independent of the preceding sections and are essential reading along with §5.1, §5.2, and §5.3 ...
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1981
Da die Kugelfunktionen eine wichtige Rolle bei speziellen Problemen der Potentialtheorie spielen (vgl. z.B. [24],[30),[52]), bietet es sich an, als Anwendung des Transformationskalkuls die Laplace -Differentialgleichung ∆U =O zu untersuchen. Mit ∆ ist hier der ubliche dreidimensionale Laplace — Differentialoperator: $$ \Delta : = \frac{{{d^2 ...
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Da die Kugelfunktionen eine wichtige Rolle bei speziellen Problemen der Potentialtheorie spielen (vgl. z.B. [24],[30),[52]), bietet es sich an, als Anwendung des Transformationskalkuls die Laplace -Differentialgleichung ∆U =O zu untersuchen. Mit ∆ ist hier der ubliche dreidimensionale Laplace — Differentialoperator: $$ \Delta : = \frac{{{d^2 ...
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A-to-Z Guide to Thermodynamics, Heat and Mass Transfer, and Fluids Engineering, 2006
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