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- Title
PARABOLIC EQUATIONS WITH p, q-GROWTH: THE SUBQUADRATIC CASE.
- Authors
SINGER, THOMAS
- Abstract
We are interested in existence and regularity results for weak solutions of parabolic equations of the type ∂tu - div a(x, t, Du) = 0 on a parabolic space time cylinder ΩT. The vector field a is assumed to satisfy a non-standard p, q-growth condition. We treat the subquadratic case, where ... holds. We show existence of weak su ∈ Lp(0,T;W1,p(Ω))∩Llocq(0,T;Wloc1,q(Ω)) for the Cauchy-Dirichlet problem associated to the parabolic equation from above. Further, a local bound for the spatial gradient Du is established. The results cover for example equations of the type ... with μ ∈ [0,1] and suitable functions α(x,t) and β(x,t). We emphasize that the results cover the singular case μ = 0.
- Subjects
ELLIPTIC equations; DIRICHLET problem; CAUCHY problem; MATHEMATICAL bounds; LAPLACIAN matrices
- Publication
Quarterly Journal of Mathematics, 2015, Vol 66, Issue 2, p707
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/hav005