Probabilistic approach to singular perturbations of semilinear and quasilinear parabolic PDEs
β Scribed by Philippe Briand; Ying Hu
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 143 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0362-546X
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π SIMILAR VOLUMES
Suppose 1<: 2, L is a second-order elliptic differential operator in R d and D is a bounded smooth domain in R d . Let Q=R + \_D and let 1 be a compact set on the lateral boundary of Q. We prove that 1 is a removable lateral singularity for the equation u\* +Lu=u : in Q if and only if Cap 1Γ:, 2Γ:,
We study the limit of the solution of linear and semilinear second order PDEs of parabolic type, with rapidly oscillating periodic coefficients, singular drift, and singular coefficient of the zeroth order term. Our method of proof is fully probabilistic and builds upon the arguments in earlier work
with 1 < p < n+2 n-2 , n 2, and 0 V (x) β L β , which may decay to 0 at infinity. We prove that if V is radial and satisfies then (1) admits a (ground state) positive solution. We do not use traditional variational methods and the result relies on the study of global solutions of the parabolic prob