Renormalized solutions of the fractional Laplace equation

Abstract: We define renormalized solutions for the problems of the kind in , . Here β is a maximal monotone graph in , and , , is the fractional Laplace operator which is a particular case of Lévy diffusions. We prove well-posedness in the framework of renormalized solutions. Then the Cauchy problem for the associated evolution equations can be solved using the Crandall–Liggett semigroup technique. [ABSTRACT FROM AUTHOR]