A CLASSICAL APPROACH FOR THE p-LAPLACIAN IN OSCILLATING THIN DOMAINS

Autor(es)

Nakasato, Jean Carlos ^[1] ; Pereira, Marcone Correa ^[2]

Afiliação do(s) autor(es)

^[1] Univ Zagreb, Fac Sci, Dept Math, Zagreb - Croatia

^[2] Univ Sao Paulo, Dept Matemat Aplicada, IME, Rua Matao 1010, Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS; v. 58, n. 1, p. 209-231, SEP 2021.
• Citações Web of Science: 0

Resumo

In this work we study the asymptotic behavior of solutions to the p-Laplacian equation posed in a 2-dimensional open set which degenerates into a line segment when a positive parameter epsilon goes to zero (a thin domain perturbation). Also, we notice that oscillatory behavior on the upper boundary of the region is allowed. Combining methods from classic homogenization theory and monotone operators we obtain the homogenized equation proving convergence of the solutions and establishing a corrector function which guarantees strong convergence in W-1,W-p for 1 < p < +infinity. (AU)

• Processo FAPESP: 20/04813-0 - Análise assintótica e qualitativa de equações integro-diferenciais
• Beneficiário: Marcone Corrêa Pereira
• Modalidade de apoio: Auxílio à Pesquisa - Regular