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@article{1448782, author = {Marcus, Moshe and Nguyen, PhuocandTai}, article_location = {The Netherlands}, article_number = {1}, doi = {http://dx.doi.org/10.1016/j.anihpc.2015.10.001}, keywords = {Hardy potential;Martin kernel;Moderate solutions;Normalized boundary trace;Critical exponent;Removable singularities}, language = {eng}, issn = {0294-1449}, journal = {Annales de l'Institut Henri Poincaré. Analyse Non Linéaire}, title = {Moderate solutions of semilinear elliptic equations with Hardy potential}, url = {http://dx.doi.org/10.1016/j.anihpc.2015.10.001}, volume = {34/2017}, year = {2015} }
TY - JOUR ID - 1448782 AU - Marcus, Moshe - Nguyen, Phuoc-Tai PY - 2015 TI - Moderate solutions of semilinear elliptic equations with Hardy potential JF - Annales de l'Institut Henri Poincaré. Analyse Non Linéaire VL - 34/2017 IS - 1 SP - 69-88 EP - 69-88 PB - Elsevier SN - 02941449 KW - Hardy potential;Martin kernel;Moderate solutions;Normalized boundary trace;Critical exponent;Removable singularities UR - http://dx.doi.org/10.1016/j.anihpc.2015.10.001 L2 - http://dx.doi.org/10.1016/j.anihpc.2015.10.001 N2 - Let Omega be a bounded smooth domain in R-N. We study positive solutions of equation (E) - L(mu)u + u(q) = 0 in Omega where L-mu = Delta + mu/delta(2), 0 < mu, q > 1 and delta(x) = dist (x, partial derivative Omega). A positive solution of (E) is moderate if it is dominated by an L-mu-harmonic function. If mu < C-H (Omega) (the Hardy constant for Omega) every positive L-mu-harmonic function can be represented in terms of a finite measure on partial derivative Omega via the Martin representation theorem. However the classical measure boundary trace of any such solution is zero. We introduce a notion of normalized boundary trace by which we obtain a complete classification of the positive moderate solutions of (E) in the subcritical case, 1 < q < q(mu,c). (The critical value depends only on N and mu) For q >= q(mu,c) there exists no moderate solution with an isolated singularity on the boundary. The normalized boundary trace and associated boundary value problems are also discussed in detail for the linear operator L-mu. These results form the basis for the study of the nonlinear problem. ER -
MARCUS, Moshe a Phuoc-Tai NGUYEN. Moderate solutions of semilinear elliptic equations with Hardy potential. \textit{Annales de l'Institut Henri Poincaré. Analyse Non Linéaire}. The Netherlands: Elsevier, 2015, roč.~34/2017, č.~1, s.~69-88. ISSN~0294-1449. Dostupné z: https://dx.doi.org/10.1016/j.anihpc.2015.10.001.
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