Abstract
Motivated by a practical problem on a corrosion process, we shall study a third kind of BVP for a large class of elliptic equations in vector-valued L p spaces. Particularly we will determine optimal spaces for boundary data and get maximal regularity for inhomogeneous equations. Then based on these results we shall treat some nonlinear problems. Our approach will be based on the semigroup theory, the interpolation theory of Banach spaces, fractional powers of positive operators, operator-valued Fourier multiplier theorems and the Banach fixed point theorem.
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