Little holes and convergence of solutions of −Δu = u(N + 2)⧸(N - 2)

DOI10.1016/0362-546X(90)90026-DzbMath0713.35008MaRDI QIDQ3198187

Roger Lewandowski

Publication date: 1990

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

convergencecritical Sobolev exponentblow upDirac masslittle hole

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (13)

Problem with critical Sobolev exponent and with weight ⋮ Sign changing solutions to a nonlinear elliptic problem involving the critical Sobolev exponent in pierced domains ⋮ A critical elliptic problem involving fractional Laplacian operator in domains with shrinking holes ⋮ On Limits Of Solutions Of Elliptic Problems With Nearly Critical Exponent ⋮ Coron's problem for the critical Lane-Emden system ⋮ An elliptic problem with critical growth in domains with shrinking holes. ⋮ A nonexistence result for a nonlinear equation involving critical Sobolev exponent ⋮ Single blow-up solutions for a slightly subcritical biharmonic equation ⋮ Solutions positives de l'équation $- \Delta u = u^p + \mu u^q$ dans un domaine à trou ⋮ Multipeak solutions to the Bahri-Coron problem in domains with a shrinking hole ⋮ A fountain of positive bubbles on a Coron's problem for a competitive weakly coupled gradient system ⋮ On Blow-Up of Positive Solutions for A Riharmonic Equation Involving Nearly Critical Exponent ⋮ Multiple solutions to the Bahri–Coron problem in domains with a shrinking hole of positive dimension

Cites Work

• A global compactness result for elliptic boundary value problems involving limiting nonlinearities
• Convergence of solutions of H-systems or how to blow bubbles
• The existence of minimal immersions of 2-spheres
• Large solutions to the volume constrained Plateau problem
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
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