Displaying similar documents to “Accurate WKB Approximation for a 1D Problem with Low Regularity”

Control-theoretic properties of structural acoustic models with thermal effects, II. Trace regularity results

Francesca Bucci (2008)

Applicationes Mathematicae

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We consider a structural acoustic problem with the flexible wall modeled by a thermoelastic plate, subject to Dirichlet boundary control in the thermal component. We establish sharp regularity results for the traces of the thermal variable on the boundary in case the system is supplemented with clamped mechanical boundary conditions. These regularity estimates are most crucial for validity of the optimal control theory developed by Acquistapace et al. [Adv. Differential Equations, 2005],...

On the normal variations of a domain

D. Bresch, J. Simon (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In domain optimization problems, normal variations of a reference domain are frequently used. We prove that such variations do not preserve the regularity of the domain. More precisely, we give a bounded domain which boundary is m times differentiable and a scalar variation which is infinitely differentiable such that the deformed boundary is only m-1 times differentiable. We prove in addition that the only normal variations which preserve the regularity are those with constant magnitude....

Regularity and optimal control of quasicoupled and coupled heating processes

Jiří Jarušek (1996)

Applications of Mathematics

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Sufficient conditions for the stresses in the threedimensional linearized coupled thermoelastic system including viscoelasticity to be continuous and bounded are derived and optimization of heating processes described by quasicoupled or partially linearized coupled thermoelastic systems with constraints on stresses is treated. Due to the consideration of heating regimes being “as nonregular as possible” and because of the well-known lack of results concerning the classical regularity...

Solutions of the constraint equations in general relativity satisfying "hyperboloidal boundary conditions"

Andersson Lars, Chruściel Piotr T.

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Abstract We prove existence of the solutions of the constraint equations satisfying "hyperboloidal boundary conditions" using the Choquet-Bruhat-Lichnerowicz-York conformal method and we analyze in detail their differentiability near the conformal boundary. We show that generic "hyperboloidal initial data" display asymptotic behaviour which is not compatible with Penrose's hypothesis of smoothness of ℐ. We also show that a large class of "non-generic" initial data...

Weak uniqueness and partial regularity for the composite membrane problem

Sagun Chanillo, Carlos E. Kenig (2008)

Journal of the European Mathematical Society

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We study the composite membrane problem in all dimensions. We prove that the minimizing solutions exhibit a weak uniqueness property which under certain conditions can be turned into a full uniqueness result. Next we study the partial regularity of the solutions to the Euler–Lagrange equation associated to the composite problem and also the regularity of the free boundary for solutions to the Euler–Lagrange equations.