We prove optimal integrability results for solutions of the p(·)-Laplace equation in the scale of (weak) Lebesgue spaces. To obtain this, we show that variable exponent Riesz and Wolff potentials map L to variable exponent weak Lebesgue spaces.

We prove a boundary Harnack principle in Lipschitz domains with small constant for fully nonlinear and $p$-Laplace type equations right hand side, as well the Laplace equation on nontangentially accessible under extra conditions. The approach is completely new gives systematic proving similar results variety of geometries.

reduced differental transform method (rdtm), which isone of the useful and effective numerical method, is applied to solve nonlinear time-dependent foam drainage equation (fde) with different initial conditions. we compare our method with the famous adomian decomposition and laplace decomposition methods. the obtained resultsdemonstrated that rdtm is a powerful tool for solving nonlinear par...

We study the global solution curves, and prove the existence of infinitely many positive solutions for three classes of self-similar equations, with p-Laplace operator. In case p = 2, these are well-known problems involving the Gelfand equation, the equation modeling electrostatic micro-electromechanical systems (MEMS), and a polynomial nonlinearity. We extend the classical results of D.D. Jose...

Recently, amount of work about the A-harmonic equation for the differential forms has been done. In fact, the A-harmonic equation is an important generalization of the p-harmonic equation in R, p > 1, and the p-harmonic equation is a natural extension of the usual Laplace equation see 1 for the details . The reverse Hölder inequalities have been widely studied and frequently used in analysis an...