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I studied linear elliptic, parabolic and hyperbolic PDEs (boundary/initial value problem) in terms of existence, uniqueness and regularity. I studied always, following Evans book "PDE", the case with zero boundary value. I've tried to repeat some energy estimates with non zero boundary value and I got some results that i wanna check. Where could I find references for this kind of problems?

Thanks for the help, Marco Menale

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The book by Demengel and Demengel has exactly what you seek.

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It's difficult for me to check the details at the moment, but the book Non-Homogeneous Boundary Value Problems and Applications by Lions and Magenes might also be helpful, perhaps more so for elliptic problems.

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