BEGIN:VCALENDAR METHOD:PUBLISH PRODID:en-www-math-fau-de//Events//EN VERSION:2.0 BEGIN:VEVENT SUMMARY:Kolloquium: Wolfgang Arendt (Universität Ulm): The Dirichlet Problem Without the Maximum Principle UID:30b92cd2-6381-483b-9a2f-e57b102d51b0 DESCRIPTION:The Dirichlet Problem Without the Maximum Principle – \; Vortragender: Wolfgang Arendt\, Universität Ulm –\; Einladend er: E. Wiedemann Abstract: In the first part of the talk we recall kno wn results on the Dirichlet problem for the Laplacian. We will mention the Dirichlet Principle\, the Perron solution\, Wiener’\;s chara cterization of well-posedness via a capacity condition and several fur ther beautiful results. The fundamental De Giorgi-Nash Theorem allowed Stampacchia and coauthors to extend many of these results to elliptic operators (instead of the Laplacian). For these generalizations the m aximum principle plays an important role\; it is valid only if the coe fficients of the operator satisfy a certain divergence condition. In 2 019 we succeeded to prove many of the well-posedness results without t hat the maximum principle holds. The only condition we need is that 0 is not a Dirichlet eigenvalue\, which is equivalent to uniqueness in t he Dirichlet problem. The Perron solution is a special challenge in th is general setting\, and diverse equivalent descriptions could be give n recently. The most interesting one is even new for the Laplacian. Th ese results are contained in the following two articles: W. Arendt\, T . ter Elst: The Dirichlet Problem without the Maximum Principle. Ann. Inst. Fourier\, Grenoble\, 69 (2019) 763-782. W. Arendt\, T. ter Elst\ , M. Sauter: The Perron Solution for Elliptic Equations without the Ma ximum Principle. Math. Ann. 2024. DTSTART:20240430T143000Z DTEND:20240430T153000Z LOCATION:Hörsaal H13\, Cauerstr. 11\, 91058 Erlangen DTSTAMP:20260730T030737Z END:VEVENT END:VCALENDAR