Nonlinear Potential Theory for elliptic equations Abubakar Mwasa - - PowerPoint PPT Presentation

Nonlinear Potential Theory for elliptic equations Abubakar Mwasa

Department of Mathematics, Link¨

• ping University

Department of Mathematics, Busitema University

First Network Meeting for Sida- and ISP-funded PhD Students in Mathematics Stockholm 7–8 March 2017

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My Advisors

Jana Bj¨

• rn

Anders Bj¨

• rn
• V. Ssembatya

G.I Mirumbe

Main advisor Assistant advisor Assistant advisor Assistant advisor Link¨

• ping

Link¨

• ping

Makerere Makerere

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Nonlinear elliptic equations in unbounded domains via inversions

Minimisation of energy using pde e.g. Laplace equation ∆u = 0 which is equivalent to minimising energy integral

• Ω |∇u|2dx.

Cousin form: Nonlinear (p−Laplace) equation for nonlinear situations ∆pu := div(|∇u|p−2∇u) = 0; 1 < p < ∞ Problem: Consider a mixed BVP for p−Laplace equation in an open half infinite cylinder in Rn.

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Schematic representation of the intended problem

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Tools and Expectations

Main aim: Establish the behaviour of weak solutions at ∞. Apply tools from pdes on bounded domains to obtain results. Generalise [1] to the nonlinear situation and will contribute to the understanding of boundary regularity on infinite domains Gradually move towards potential theory and pdes on metric spaces. Acquire and extend the research skills in the field of potential theory to my home university.

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Reference

1 Bj¨

• rn, A.: Regularity at infinity for a mixed problem for

degenerate elliptic operators in a half cylinder. Math. Scand. 81, 101-126(1997)

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Tack s˚ a mycket! Thank you!

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