Mild solutions of semilinear elliptic equations in Hilbert spaces

@article{Federico2016MildSO,
  title={Mild solutions of semilinear elliptic equations in Hilbert spaces},
  author={Salvatore Federico and Fausto Gozzi},
  journal={arXiv: Analysis of PDEs},
  year={2016}
}
  • Salvatore Federico, Fausto Gozzi
  • Published 2016
  • Mathematics
  • arXiv: Analysis of PDEs
  • This paper extends the theory of regular solutions ($C^1$ in a suitable sense) for a class of semilinear elliptic equations in Hilbert spaces. The notion of regularity is based on the concept of $G$-derivative, which is introduced and discussed. A result of existence and uniqueness of solutions is stated and proved under the assumption that the transition semigroup associated to the linear part of the equation has a smoothing property, that is, it maps continuous functions into $G… CONTINUE READING

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 80 REFERENCES