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ON THE DEGENERATE $(p,q)$-LAPLACE EQUATIONS CORRESPONDING TO AN INVERSE SPECTRAL PROBLEM

Ya. Sh. Ilyasov

Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa



Abstract: The report will discuss two interrelated topics: 1) a new class of applied problems leading to equations with (p,q)-Laplace; 2) the inverse optimal problem method which is a new apparatus that allows to prove the existence, uniqueness and stability of solutions to nonlinear boundary value problems. As a model example, we will consider a boundary value problem for an equation with (p,q)-Laplace and measurable unbounded coefficients of the form:
div(σ(x)|∇u|^ {q−2}∇u) + div(|∇u|^{ p−2}∇u) = λρ(x)|u|^{q−2}u , p > q
As a spectral problem for which the inverse optimal problem method will be applied, we will consider
L_{σ}(ϕ) := −div(σ(x)|∇ϕ|^ {q−2}∇ϕ) = λρ(x)|ϕ|^{q−2}ϕ.

Website: https://teams.microsoft.com/l/meetup-join/19%3ameeting_YzMyMjgxMjktYTY5ZC00M2Y4LWIzYTgtNDVjNTMxZTM1Njhh%40thread.v2/0?context=%7b%22Tid%22%3a%222ae95c20-c675-4c48-88d3-f276b762bf52%22%2c%22Oid%22%3a%2266c4b047-af30-41c8-9097-2039bac83cbc%22%7d


© Steklov Math. Inst. of RAS, 2024