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An elliptic problem with critical growth in domains with shrinking holes. (English) Zbl 1086.35046

Summary: We study an elliptic problem involving critical Sobolev exponent in domains with small holes. We prove the existence of solutions which blow up like a volcano near the centre of each hole.

MSC:

35J60 Nonlinear elliptic equations
35B33 Critical exponents in context of PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
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