Integral boundary value problem shows existence and uniqueness of solutions for nonlinear elliptic problems, highlighting maximal regularity properties in Lp-spaces.
Integral boundary value problem for abstract elliptic equation with variable coefficients is studied. The uniform maximal regularity properties and Fredholmness of this problem are obtained in vector-valued Lp-spaces. It is proven that the corresponding differential operator is positive and is a generator of an analytic semigroup. Then we derive the existence and uniqueness of the solution for the nonlinear elliptic problem. In application, the maximal regularity properties of Cauchy problem for abstract parabolic equation and anisotropic elliptic equations are established.
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Veli Shakhmurov (2025) studied this question.
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