# 東京理科大学理工学部 数学科

seminar:2014:009

### 第09回

• 講演者： Giuseppe Di Fazio 氏(カターニア大学）
• 題目：Strong $A_\infty$ weights and quasilinear degenerate elliptic equations
• 日時：平成26年9月10日（水）10:30–11:30

Strong $A_\infty$ weights are introduced and degenerate elliptic equations with respect to strong weights are then studied. We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions. The degeneracy is given by a suitable power of a strong $A_\infty$ weight. Regularity results are achieved under minimal assumptions on the coefficients. Then we point two applications. First we prove $C^{1,\alpha}$ local estimates for solutions of a degenerate equation in non divergence form. As a second application we prove a unique continuation property for positive weak solutions of degenerate elliptic equations.

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seminar/2014/009.txt · 最終更新: 2017/11/16 18:24 (外部編集)