Strong solutions of quasilinear integro-differential equations with singular kernels in several space dimensions.(English)Zbl 0813.45004

For quasilinear integro-differential equations of the form $$u_ t - a^* A(u) = f$$, where $$a$$ is a scalar singular integral kernel that behaves like $$t^{-\alpha}$$, $$1/2 \leq \alpha < 1$$ and $$A$$ is a second order quasilinear elliptic operator in divergence form, solutions are found for which $$A(u)$$ is integrable over space and time.
Reviewer: H.Engler

MSC:

 45K05 Integro-partial differential equations 45G05 Singular nonlinear integral equations
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