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Solutions for Quasilinear Nonsmooth Evolution Systems in Lp
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Weierstrass Inst. Appl. Anal./S., Mohrenstr. 39, D-10117 Berlin, Germany.
Weierstrass Inst. Appl. Anal./S., Mohrenstr. 39, D-10117 Berlin, Germany.
Weierstrass Inst. Appl. Anal./S., Mohrenstr. 39, D-10117 Berlin, Germany.
2004 (English)In: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 171, no 2, 219-262 p.Article in journal (Refereed) Published
Abstract [en]

We prove that nonsmooth quasilinear parabolic systems admit a local solution in Lp strongly differentiable with respect to time over a bounded three-dimensional polyhedral space domain. The proof rests essentially on new elliptic regularity results for polyhedral Laplace interface problems for anisotropic materials. These results are based on sharp pointwise estimates for Green's function, which are also of independent interest. To treat the nonlinear problem, we then apply a classical theorem of Sobolevskii for abstract parabolic equations and recently obtained resolvent estimates for elliptic operators and interpolation results. As applications we have in mind primarily reaction-diffusion systems. The treatment of such equations in an Lp context seems to be new and allows (by Gauss' theorem) the proper definition of the normal component of currents across the boundary.

Place, publisher, year, edition, pages
2004. Vol. 171, no 2, 219-262 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-45827DOI: 10.1007/s00205-003-0297-yOAI: oai:DiVA.org:liu-45827DiVA: diva2:266723
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13

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Maz´ya, Vladimir G.

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