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On a fractional Dirichlet problem
2012 17th International Conference on Methods & Models in Automation & Robotics (MMAR), 2012In the paper a fractional analogon of the classical Dirichlet problem is considered. Using some variational method a theorem on the existence and uniqueness of solution is proved. In the proof of the main result we use a characterization of the weak convergence in the space of solutions and a fractional counterpart of du Bois-Reymond lemma.
Rafal Kamocki, Marek Majewski
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Polyharmonic dirichlet problems
Proceedings of the Steklov Institute of Mathematics, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Begehr, H., Vu, T. N. H., Zhang, Z.-X.
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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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