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INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH (IISER) PUNE
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An Autonomous Institution, Ministry of Human Resource Development, Govt. of India
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Seminars and Colloquia

Mathematics

Boundary value problem with measures for semi linear elliptic equations with Hardy potential 
 
Tue, Jan 15, 2019,   11:00 AM to 12:00 PM at Madhava Hall

Dr. Phuoc-Tai Nguyen
Masaryk University, Brno, Czech Republic

In this talk, I will discuss positive solutions of equation (E) −Lµu +
uq = 0 in Ω where Ω is a bounded smooth domain in R
N , δ(x) = dist (x, ∂Ω),
Lµ = ∆ + µ
δ
2, µ > 0, q > 1. I will introduce a notion of normalized boundary trace
to obtain a classification of positive solutions of (E) with measure boundary value
in the subcritical case 1 < q < qN,µ. (The critical value qN,µ depends only on N
and µ.) For q ≥ qN,µ, I will show that there exists no solution with an isolated
singularity on the boundary.

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