2018-09-052018-08-10ROCHA, F. S. Desigualdade de Adams em domínios ilimitados. 2018. 86 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2018.http://repositorio.bc.ufg.br/tede/handle/tede/8859In this work our aim is to present an extension of the Trudinger-Moser inequality [20] in unbounded domains of Rn for Sobolev Spaces involving high order derivatives. This inequality is nowadays known as Adams-type inequality [1]. We study the techniques developed in the works due to F. Sani and B. Ruf in [23] and due to N. Lam and G. Lu in [16] which are, essentially, combinations of the Comparison Principle of Trombetti and Vazquez for polyharmonic operators and a symmetrization argument, also known as Schwarz Symmetrization. "With such techniques in hands", our aim is to reduce our problem to the radial case and, as a consequence, find an upper bound for the supremum over all functions belonging to the unit ball of Wn;mn (Rn) provided with some specific norm, as well as the sharpness of the constant that appears in Adams inequalities.application/pdfAcesso AbertoDesigualdade de AdamsCrescimento críticoDesigualdade de Trudinger-MoserEspaços de SobolevSimetrização de SchwarzAdams inequalityCritical growthTrudinger-Moser inequalitySobolev spacesSchwarz symmetrizationCIENCIAS EXATAS E DA TERRA::MATEMATICADissertação