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It is not homogeneous and this feature turns out to impose some technical difficulties in applying usual elliptic methods for obtaining the existence and regularity of weak solutions of problems involving this operator.
In this paper we present a new approach, the so-called p-regularity method, and show that this approximate method works well and is effective.
However, differences in oral health by payment method were found to be largely attributable to socio-demographic factors and regularity of dental attendance rather then method of payment itself [ 18].
Wang and Wang [9] proved the existence of viscosity solutions by the approximation procedure and the nonlinear perturbation method, and they also obtained the regularity of the viscosity solutions.
In this case methods from the calculus of variations can be used and regularity of solutions can be shown.
The existence and regularity of the unique solution w can be proved by applying classical methods, for instance, the method of continuity (see [29]).
Our computational method is presented along with measures against possible problems regarding pollution, stability, and regularity.
In [7], Luo and Pu obtained the existence and regularity of solutions to 3He-4He system by using the Galerkin method.
The local interpretation of the rank-order method does satisfy regularity and IIA but fails to satisfy the consistency condition because to determine the ranking over a set of actual fates A, only the lineages' propensities restricted to A are taken into account (no information about their propensities over the potential-but-not-actually-considered fates is used).
"Two words: explosive and regularity".
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com