There are conditions that you must be aware of in relation to your soon-to-be former employer, because there is something called a duty of loyalty (loyalitetspligt).
Duty of loyalty means that you, as a soon-to-be former employee who is still in the notice period and is paid by an employer, must not harm your soon-to-be former employer.
Therefore, you can e.g. don't just go out and start a competing company during your notice period, and in your new company you may not use trade secrets from your previous company either - the latter follows from the Danish Marketing Act.
Your employer has the right to dismiss you if you breach the duty of loyalty, for example if you start a competing business during your notice period. This means that you may be dismissed from your workplace and not be paid for the last part of your notice period.
Your employer also has the right to demand compensation from you for any losses that you have caused in your competing company.
If you "just" start up as self-employed during the notice period, without it being a competing company, the duty of loyalty is not a problem, but there may still be restrictions or consequences for e.g. your salary during the notice period, limitations in your contract, etc.
The duty of loyalty therefore places some restrictions on what you may do to start up your new, competing business as long as you still receive a salary from your former employer in relation to competing actions that could potentially harm your soon-to-be former employer.
For example, you must not market your competing company, start selling products or services, have a published website or influence your employer's employees.
On the other hand, you are allowed to do things that do not compromise your employer.
If the business you want to start up is not competing, there may be an opportunity to start up during the notice period, while you are, for example, released from your duties.
If you are considering starting a business during a notice period, it is a good idea to contact IDA to get advice on, for example, possible consequences for your salary during the notice period if you start as self-employed, as well as other consequences.
It is not completely black and white what you are allowed to do in relation to the use of social media during the start-up of your business. Your employer will be able to argue that if you use social media it is marketing your company, and then you are violating the duty of loyalty.
The employer may also choose to regulate your use of social media as long as you are on the employer's payroll.
If you want to start a business in the same industry as your former workplace, it is always a good idea to stay good friends with your former employer.
Especially in Denmark, most industries are very small, and bad rumors spread quickly. Furthermore, you never know if you will later need help, sparring and networking via your former workplace.
So even though most things are legislated, use your common sense, treat everyone with respect and don't close any doors.
It may be that you and your employer have entered into customer or competition clauses that specifically regulate what you may and may not do when you no longer work for the company.
If you are in doubt about which rules apply in your situation as a self-employed person, you are always welcome to contact IDA's legal advice.