TY - JOUR
T1 - The Blow Up Locus of Nonlinear Elliptic Equations with Supercritical Exponents
AU - Songbo Hou 
JO - Journal of Partial Differential Equations
VL - 3
SP - 264
EP - 282
PY - 2004
DA - 2004/08
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5392.html
KW - Blow up locus
KW - Hausdorff dimension
KW - monotonicity inequality
AB - <p>We consider the compactness theorem for the positive solutions of the equation Δu + h_1u^α + h_2u^β = 0 in Ω ⊂ R^n and obtain the measure estimate of the blow up set for positive smooth solutions {u_i} of the above equation with {||u_i||_{H¹(Ω)} + ||u_i||_{L^{α+1}(Ω)} + ||u_i||_L^{β+1}(Ω)} bounded.</p>