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A semilinear PDE with free boundary

Fotouhi, M ; Sharif University of Technology | 2017

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  1. Type of Document: Article
  2. DOI: 10.1016/j.na.2016.11.019
  3. Publisher: Elsevier Ltd , 2017
  4. Abstract:
  5. We study the semilinear problem Δu=λ+(x)(u+)q−1−λ−(x)(u−)q−1inB1, from a regularity point of view for solutions and the free boundary ∂{±u>0}. Here B1 is the unit ball, 10} and Γ−=∂{u<0}, tangential to each other. It is noteworthy that the above problem (in contrast to the case q=1) introduces interesting and quite challenging features, that are not encountered in the case q=1. E.g. one obtains homogeneous global solutions that are not one-dimensional. This complicates the analysis of the free boundary substantially. © 2016 Elsevier Ltd
  6. Keywords:
  7. Regularity ; Mathematical techniques ; Nonlinear analysis ; Free boundary ; Global solutions ; Higher dimensions ; Homogeneous solutions ; Local regularity ; Nocv1 ; One-dimensional solutions ; Semilinear elliptic equation ; Differential equations
  8. Source: Nonlinear Analysis, Theory, Methods and Applications ; Volume 151 , 2017 , Pages 145-163 ; 0362546X (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0362546X16302991