The extinction versus the blow-up: Global and non-global existence of solutions of source types of degenerate parabolic equations with a singular absorption.
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DOI: 10.1016/j.jde.2017.07.029
Abstract: Abstract We consider nonnegative solutions of degenerate parabolic equations with a singular absorption term and a source nonlinear term: ∂ t u − ( | u x | p − 2 u x ) x… read more here.
Keywords: existence; equations singular; source; parabolic equations ... See more keywords
A Zvonkin's transformation for stochastic differential equations with singular drift and applications
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DOI: 10.1016/j.jde.2021.06.031
Abstract: Abstract In this paper, by establishing the localized L p - L q estimate and Sobolev estimates for parabolic partial differential equations with a singular first order term and a Lipschitz first order term, a… read more here.
Keywords: stochastic differential; singular drift; equations singular; differential equations ... See more keywords
Existence and boundary behavior of solutions of Hessian equations with singular right-hand sides
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DOI: 10.1016/j.jfa.2019.02.018
Abstract: Abstract In this paper, we establish the existence of viscosity solutions of Hessian equations with singular right-hand sides and obtain the asymptotic boundary behavior of solutions. The asymptotic results generalize those for Poisson equations and… read more here.
Keywords: solutions hessian; hessian equations; hand sides; equations singular ... See more keywords
Linear Equations in Singular Moduli
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DOI: 10.1093/imrn/rny216
Abstract: We establish an effective version of the André–Oort conjecture for linear subspaces of $Y(1)^n_{\mathbb{C}} \approx \mathbb{A}_{\mathbb{C}}^n$. This gives the first effective nontrivial results of André–Oort type for higher-dimensional varieties in products of modular curves. read more here.
Keywords: equations singular; singular moduli; linear equations;
Subelliptic equations with singular nonlinearities on the Heisenberg group
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DOI: 10.1186/s13661-018-0925-y
Abstract: AbstractIn this paper, we consider the Dirichlet boundary value problem to singular semilinear subelliptic equation on the Heisenberg group −ΔHu=1uγ+f(u),γ>0.$$-\Delta_{\mathbb{H}}u=\frac{1}{u^{\gamma}}+f(u), \quad \gamma>0. $$ We prove the positivity and continuity up to the boundary for the… read more here.
Keywords: subelliptic equations; equations singular; singular nonlinearities; group ... See more keywords