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Volume 17, Issue 3
The Blow Up Locus of Nonlinear Elliptic Equations with Supercritical Exponents

Songbo Hou

J. Part. Diff. Eq., 17 (2004), pp. 264-282.

Published online: 2004-08

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  • Abstract

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.

  • Keywords

Blow up locus Hausdorff dimension monotonicity inequality

  • AMS Subject Headings

35B45 35J20

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JPDE-17-264, author = {Songbo Hou }, title = {The Blow Up Locus of Nonlinear Elliptic Equations with Supercritical Exponents}, journal = {Journal of Partial Differential Equations}, year = {2004}, volume = {17}, number = {3}, pages = {264--282}, abstract = {

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.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5392.html} }
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 -

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.

Songbo Hou . (2004). The Blow Up Locus of Nonlinear Elliptic Equations with Supercritical Exponents. Journal of Partial Differential Equations. 17 (3). 264-282. doi:
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