String to LocalDate

As you use Joda Time, you should use DateTimeFormatter:

final DateTimeFormatter dtf = DateTimeFormatter.ofPattern("yyyy-MMM-dd");
final LocalDate dt = dtf.parseLocalDate(yourinput);

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If using Java 8 or later, then refer to hertzi's answer

You may have to go from DateTime to LocalDate.

Using Joda Time:

DateTimeFormatter FORMATTER = DateTimeFormat.forPattern("yyyy-MMM-dd");
DateTime dateTime = FORMATTER.parseDateTime("2005-nov-12");
LocalDate localDate = dateTime.toLocalDate();

java.time

Since Java 1.8, you can achieve this without an extra library by using the java.time classes. See Tutorial.

DateTimeFormatter formatter = DateTimeFormatter.ofPattern("yyyy-MMM-dd");
formatter = formatter.withLocale( putAppropriateLocaleHere );  // Locale specifies human language for translating, and cultural norms for lowercase/uppercase and abbreviations and such. Example: Locale.US or Locale.CANADA_FRENCH
LocalDate date = LocalDate.parse("2005-nov-12", formatter);

The syntax is nearly the same though.