Global Compactness Properties of Semilinear Elliptic Equations with Critical Exponential Growth

By Adimurthi, Michael Struwe. 2000

149 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/227d617bca38822153696baec4929864cb8db44f

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Critical and subcritical elliptic systems in dimension two (2004, background): “The case of a single semilinear elliptic equation in bounded subsets of R2 has been investigated by several authors, see for example [ 2 , 3, 5, 6]. It has been observed that criticality in dimension two is connected with the imbedding of H1 0N⁄O in an Orlicz spaceL’ when’NtOEe t”
New solutions for Trudinger–Moser critical equations in R2 (2010, background): “Our choice of first approximations to bubbling solutions is inspired by the discovery of the blow-up shapes first in [5] then in [2,14].”
A global compactness result for singular elliptic problems involving critical Sobolev exponent (2002, background): “Struwe in [1] have studied the convergence of (P.”
Sharp singular Adams inequalities in high order Sobolev spaces (2011, unknown): “We refer the interested reader to [13], [16], [3], [7], [6], [9], [11], [8], [20], [21], [19], [27, 28], [49], [50] and the references therein.”
Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications ✩ (2012, background): “Here we just mention some of them, we refer the reader to [17,26,55,3–5,22–24,51,50,40,61,67,71] and the references therein.”
A Sharp Trudinger-Moser Type Inequality for Unbounded Domains in Rn (2006, methodology): “We will use the ideas from [L1] and [L2] (see also [A-M] and [A-D]).”
Asymptotic estimates for a two-dimensional problem with polynomial nonlinearity (2003, methodology): “Here we use the two-dimensional blow-up technique introduced in [1].”
Blow-up Analysis in Dimension 2 and a Sharp Form of Trudinger–Moser Inequality (2005, background): “We present here a more direct proof of (3.15) than the proof of Adimurthi and Struwe (2000).”
Improved Moser-Trudinger Inequality Involving Lp Norm in n Dimensions (2014, unknown): “This approach for elliptic equations related to the classical Moser-Trudinger inequality was initiated in [3],[2], [10] and [1].”
Critical points of the Moser-Trudinger functional on a disk (2012, background): “Druet proved (see also [4] and [2] for previous related results, where the blow-up profile was identified, and [16] where the parabolic case was treated): let (uk) be a sequence of solutions to (4) with Λk ≤ C and supB1 uk → ∞.”
Existence and asymptotics for solutions of a non-local Q-curvature equation in dimension three (2013, background): “, [1, 2, 10, 12, 19, 22, 26, 31], or the equation P 2m g u+Qg = Qe 2mu on a manifold (M, g) (13) which prescribes the Q-curvature of the manifold (M, e2ug), see, e.”