A sharp form of an embedding into exponential and double exponential spaces

Concentration–compactness Principle for Embedding into Multiple Exponential Spaces

Let Ω⊂Rn , n 2 , be a bounded domain and let α < n−1 . We prove the ConcentrationCompactness Principle for the embedding of the Orlicz-Sobolev space W 1 0 L n logn−1 L logα logL(Ω) into the Orlicz space corresponding to a Young function that behaves like exp(exp(t n n−1−α )) for large t . We also give the result for the case of the embedding into triple and other multiple exponential spaces. Ma...

EXPONENTIAL MAP OF A CLASS OF TOP SPACES

Double Exponential

Nonlinear propagation of an asymmetric double exponential

A weak-shock solution is obtained for the nonlinear propagation of a waveform that initially has the form of an asymmetric double exponential. Such a wave shocks at its peak, so that shock growth and wave-amplitude attenuation occur simultaneously. Simple formulas for wave amplitude, shock amplitude, and arrival time are given as is an expression for the waveform. We also present a general tech...

Solution of Troesche's problem by double exponential Sinc collocation method

In this investigation, the Sinc collocation method based on double exponential transformation is developed to solve the Troesche's problem. Properties of this method are utilized to reduce the system of strongly nonlinear two point boundary value problem to same nonlinear algebraic equations. Combining double exponential transformation through Sinc collocation method causes the remarkable resul...