108 citations · 294 across the 20 of their papers we have counts for
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Sharp long distance upper bounds for solutions of Leibenson's equation on Riemannian manifolds
Alexander Grigor'yan, Jin Sun, Philipp Sürig
We consider on Riemannian manifolds the Leibenson equation that is also known as a doubly nonlinear evolution equation. We prove sharp upper estimates o…
Superlinear elliptic inequalities on manifolds
Alexander Grigor'yan, Yuhua Sun, Igor Verbitsky
Let be a complete non-compact Riemannian manifold and let be a Radon measure on . We study the problem of existence or non-existence of positive solutions to a semilinea…
Pointwise estimates of solutions to nonlinear equations for nonlocal operators
Alexander Grigor'yan, Igor Verbitsky
We study pointwise behavior of positive solutions to nonlinear integral equations, and related inequalities, of the type \begin{equation*} u(x) - \int_ΩG(x, y) \, g(u(y)) d σ(y) =…
Existence of positive solutions to some nonlinear equations on locally finite graphs
Alexander Grigor'yan, Yong Lin, Yunyan Yang
Let be a locally finite graph, whose measure have positive lower bound, and be the usual graph Laplacian. Applying the mountain-pass theorem due to Ambrosetti-…
Kazdan-Warner equation on graph
Alexander Grigor'yan, Yong Lin, Yunyan Yang
Let be a finite graph and be the usual graph Laplacian. Using the calculus of variations and a method of upper and lower solutions, we give various conditions such th…
Yamabe type equations on graphs
Alexander Grigor'yan, Yong Lin, Yunyan Yang
Let be a locally finite graph, be a bounded domain, be the usual graph Laplacian, and be the first eigenvalue of with respect to Dirichlet…
Pointwise estimates of solutions to semilinear elliptic equations and inequalities
Alexander Grigor'yan, Igor Verbitsky
We obtain sharp pointwise estimates for positive solutions to the equation , where is an elliptic operator in divergence form, , $f\g…