Semilinear pseudodifferential equations in spaces of tempered\n ultradistributions

2014/10/21 by Marco Cappiello, Cappiello, Marco, Stevan Pilipović +3 · 1 citation
Engineering · Mathematics · #35A17 #46F05 #47G30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1410.5717

openalex publication_date 2014/10/21 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We study a class of semilinear elliptic equations on spaces of tempered\nultradistributions of Beurling and Roumieu type. Assuming that the linear part\nof the equation is an elliptic pseudodifferential operator of infinite order\nwith a sub-exponential growth of its symbol and that the non linear part is\ngiven by an infinite sum of powers of u with sub-exponential growth with\nrespect to u, we prove a regularity result in the functional setting of the\nquoted ultradistribution spaces for a weak Sobolev type solution u.\n

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