In America, poet Emily Dickinson was also writing during this period, as were Harriet Beecher Stowe, Sarah Orne Jewett and Ellen Glasgow, among many others. When you ask about "well-known" writers, it's not clear whether you mean well known in their time, or well known now. Literary reputations can shift, so that a writer who was popular during her lifetime is now no longer read and a writer who sold few books in her day has become critically acclaimed.
George Eliot (real name Mary Ann Evans) wrote from about the late 1850s into the late 1870s.
Frances Hodgson Burnett - The Secret Garden
Johanna Spyri - the Heidi series of books
There is also a great website for little know African - American female writers in the 19th century.
Edith Wharton is one of the most important female authors of all time. She actively wrote against the haughty attitudes of the weathly New Englanders with novels like "The Age of Innocence," "Ethan Frome," and "The House of Mirth." She was also quite noted for her abilities as an interior designer/decorator. She wrote much on the subject of style and decor and published a few guides. "The Decorating of Houses" springs to mind.
Two American authors who were renowned as well as controversial during this period are Charlotte Perkins Gilman and Kate Chopin, both of whom wrote of the repression of women in their age.
Gilman's novella "The Yellow Wallpaper" (first published in 1892) brought to light the treatments of her time for postpartum depression which made light of this condition.
Like Gilman, Kate Chopin wished to expose the restrictive lives of women in the latter part of the Victorian age. Her novel "The Awakening" (published in 1899) was as controversial as Gilman's "The Yellow Wallpaper."
(Willa Cather came shortly after what you have suggested: She published the classic "My Antonia" in 1917.)
I am guessing you mean world wide and not one particular country, correct? Off the top of my head, you have George Eliot (pen name of Mary Ann Evans) who was popular from about 1850 through 1880. She was an English author.
Then you have the famed Louisa May Alcott, best known for her works Little Women, Little Men, and Jo's Boys.
Another British author to look at would be Mary Augusta Ward, author of Daphne (1909).
A popular author at the time (although the majority of her works are now sadly out of print) was Charlotte Mary Yonge.
A controversial choice might be Marie Corelli. Her works were critically savaged but she was a very popular at the time.
Florence Marryat's work focused mainly on spirituality and mediums.
I hope this helps.
Edith Wharton, Kate Chopin, and Martha Finley come to mind.