# 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} }

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

#### Citations

##### Publications citing this paper.

SHOWING 1-3 OF 3 CITATIONS

## Path-dependent equations and viscosity solutions in infinite dimension

VIEW 1 EXCERPT

CITES BACKGROUND

## Verification theorems for stochastic optimal control problems in Hilbert spaces by means of a generalized Dynkin formula

VIEW 10 EXCERPTS

CITES BACKGROUND, RESULTS & METHODS

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 80 REFERENCES