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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Interior Sobolev regularity for fully nonlinear parabolic equations

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Autor(es):
Castillo, Ricardo ; Pimentel, Edgard A.
Número total de Autores: 2
Tipo de documento: Artigo Científico
Fonte: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS; v. 56, n. 5 OCT 2017.
Citações Web of Science: 2
Resumo

In the present paper, we establish sharp Sobolev estimates for solutions of fully nonlinear parabolic equations, under minimal, asymptotic, assumptions on the governing operator. In particular, we prove that solutions are in W-loc(2,1;p). Our argument unfolds by importing improved regularity from a limiting configuration. In this concrete case, we recur to the recession function associated with F. This machinery allows us to impose conditions solely on the original operator at the infinity of S(d). From a heuristic viewpoint, integral regularity would be set by the behavior of F at the ends of that space. Moreover, we explore a number of consequences of our findings, and develop some related results; these include a parabolic version of Escauriaza's exponent, a universal modulus of continuity for the solutions and estimates in p-BMO spaces. (AU)

Processo FAPESP: 15/13011-6 - Equações diferenciais parciais não-lineares: boa colocação e teoria de regularidade
Beneficiário:Edgard Almeida Pimentel
Linha de fomento: Auxílio à Pesquisa - Regular