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Schedule, Notes/Handouts & Videos

Analysis of Partial Differential Equations (Okinawa Institute of Science and Technology) July 29, 2024 - August 09, 2024

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Jul 29, 2024
Monday
09:00 AM - 10:15 AM
  Course II – Lecture 1: "Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs"
Ugur Abdulla (Okinawa Institute of Science and Technology)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Course II – Lecture 2/Active Learning Session (als): "Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs"
Ugur Abdulla (Okinawa Institute of Science and Technology)
12:00 PM - 01:00 PM
  Lunch
01:00 PM - 02:15 PM
  Course II - Lecture 3: "Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs III"
Ugur Abdulla (Okinawa Institute of Science and Technology)
02:15 PM - 02:45 PM
  Afternoon Tea
02:45 PM - 04:00 PM
  Course II – Lecture 4/als: " Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs IV"
Ugur Abdulla (Okinawa Institute of Science and Technology)
Jul 30, 2024
Tuesday
09:00 AM - 10:15 AM
  Course I – Lecture 1: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form I"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Course I – Lecture 2/als: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form II"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
12:00 PM - 01:00 PM
  Lunch
01:00 PM - 02:15 PM
  Course I - Lecture 3: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form III"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
02:15 PM - 02:45 PM
  Afternoon Tea
02:45 PM - 04:00 PM
  Course I – Lecture 4/als: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form IV"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
Jul 31, 2024
Wednesday
09:00 AM - 10:15 AM
  Course II – Lecture 5: "Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs V"
Ugur Abdulla (Okinawa Institute of Science and Technology)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Course II – Lecture 6/ als: "Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs VI"
Ugur Abdulla (Okinawa Institute of Science and Technology)
12:00 PM - 01:00 PM
  Lunch
01:00 PM - 02:00 PM
  Plenary Lecture: TBA
Gui-Qiang Chen (University of Oxford)
02:00 PM - 02:30 PM
  Afternoon Tea
02:30 PM - 03:45 PM
  Course I - Lecture 5: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form V"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
03:45 PM - 05:00 PM
  Course I – Lecture 6/als: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form VI"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
Aug 01, 2024
Thursday
09:00 AM - 10:15 AM
  Course II – Lecture 7: "Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs VII"
Ugur Abdulla (Okinawa Institute of Science and Technology)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Course II – Lecture 8/ als: "Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs VIII"
Ugur Abdulla (Okinawa Institute of Science and Technology)
12:00 PM - 01:00 PM
  Lunch
01:00 PM - 02:15 PM
  Course I - Lecture 7: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form VII"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
02:15 PM - 02:45 PM
  Afternoon Tea
02:45 PM - 04:00 PM
  Course I – Lecture 8/als: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form VIII"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
Aug 02, 2024
Friday
09:00 AM - 10:15 AM
  Course II – Lecture 9: "Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs IX"
Ugur Abdulla (Okinawa Institute of Science and Technology)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Course II – Lecture 10/ als: "Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs "
Ugur Abdulla (Okinawa Institute of Science and Technology)
12:00 PM - 01:00 PM
  Lunch
01:00 PM - 02:00 PM
  Plenary Lecture: TBA
Juan Manfredi
02:00 PM - 02:30 PM
  Afternoon Tea
02:30 PM - 04:45 PM
  Course I - Lecture 9: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form IX"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
03:45 PM - 05:00 PM
  Course I – Lecture 10/als: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form X"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
Aug 05, 2024
Monday
09:00 AM - 10:15 AM
  Course I - Lecture 11: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form XI"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 11:45 AM
  Course I – Lecture 12/als: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form XII"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
12:00 PM - 01:00 PM
  Lunch
01:00 PM - 02:00 PM
  Plenary Lecture: "Weak convergence methods for the nonlinear PDEs I"
Lawrence Evans (University of California, Berkeley)
02:00 PM - 02:30 PM
  Afternoon Tea
02:30 PM - 03:45 PM
  Course II – Lecture 11: "Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs XI"
Ugur Abdulla (Okinawa Institute of Science and Technology)
03:45 PM - 05:00 PM
  Course II – Lecture 12/als: 'Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs XII"
Ugur Abdulla (Okinawa Institute of Science and Technology)
Aug 06, 2024
Tuesday
09:00 AM - 10:15 AM
  Course I - Lecture 13: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form XIII"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Lecture 14/als: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form XIV"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
12:00 PM - 01:00 PM
  Lunch
01:00 PM - 02:00 PM
  Plenary Lecture: "Weak convergence methods for the nonlinear PDEs II"
Lawrence Evans (University of California, Berkeley)
02:00 PM - 02:30 PM
  Afternoon Tea
02:30 PM - 04:00 PM
  Course II – Lecture 13: "Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs XIII"
Ugur Abdulla (Okinawa Institute of Science and Technology)
04:00 PM - 05:00 PM
  Course II – Lecture 14/als: "Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs XIV"
Ugur Abdulla (Okinawa Institute of Science and Technology)
Aug 07, 2024
Wednesday
09:00 AM - 10:15 AM
  Course II - Lecture 15: "Peron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs XV"
Ugur Abdulla (Okinawa Institute of Science and Technology)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Course I – Lecture 15. Gui-Qiang Chen & Monica Torres, Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form XV
12:00 PM - 01:00 PM
  Lunch
01:00 PM - 02:00 PM
  Plenary Lecture: "Kolmogorov Problem and Wiener-type criteria for the Removability of Fundamental Singularity for the Parabolic PDEs"
Ugur Abdulla (Okinawa Institute of Science and Technology)
02:00 PM - 02:30 PM
  Afternoon Tea
02:30 PM - 09:00 PM
  Field trip to Okinawa Aquarium
Aug 08, 2024
Thursday
09:00 AM - 10:15 AM
  Course I - Lecture 16: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form XVI"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Course I – Lecture 17/als: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form XVII"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
12:00 PM - 01:00 PM
  Lunch
01:00 PM - 02:15 PM
  Course II – Lecture 16: "Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs XVI"
Ugur Abdulla (Okinawa Institute of Science and Technology)
02:15 PM - 02:45 PM
  Afternoon Tea
02:45 PM - 04:00 PM
  Course II – Lecture 17/als: "Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs XVII"
Ugur Abdulla (Okinawa Institute of Science and Technology)
Aug 09, 2024
Friday
09:00 AM - 10:15 AM
  Course I - Lecture 18: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form XVIII"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Course I – Lecture 19/als: "Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form XIX"
Gui-Qiang Chen (University of Oxford), Monica Torres (Purdue University)
12:00 PM - 01:00 PM
  Lunch
01:00 PM - 02:15 PM
  Course II – Lecture 18: "Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs XVIII"
Ugur Abdulla (Okinawa Institute of Science and Technology)
02:15 PM - 02:45 PM
  Afternoon Tea
02:45 PM - 04:00 PM
  Course II – Lecture 19/als: "Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs XIX"
Ugur Abdulla (Okinawa Institute of Science and Technology)
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