We consider a one-phase Bernoulli free boundary problem in a container D – a smooth open subset of Rd– under the condition that on the fixed boundary ∂D the normal derivative of the solutions is prescribed. We study the regularity of the free boundary (the boundary of the positivity set of the solution) up to ∂D and the structure of the wetting region, which is the contact set between the free boundary and the ((d − 1)-dimensional) fixed boundary ∂D. In particular, we characterize the contact angle in terms of the permeability of the porous container and we show that the boundary of the wetting region is a smooth (d − 2)-dimensional manifold, up to a (possibly empty) closed set of Hausdorff dimension at most d − 5.
A capillarity one-phase Bernoulli free boundary problem
Ferreri, Lorenzo;
2023
Abstract
We consider a one-phase Bernoulli free boundary problem in a container D – a smooth open subset of Rd– under the condition that on the fixed boundary ∂D the normal derivative of the solutions is prescribed. We study the regularity of the free boundary (the boundary of the positivity set of the solution) up to ∂D and the structure of the wetting region, which is the contact set between the free boundary and the ((d − 1)-dimensional) fixed boundary ∂D. In particular, we characterize the contact angle in terms of the permeability of the porous container and we show that the boundary of the wetting region is a smooth (d − 2)-dimensional manifold, up to a (possibly empty) closed set of Hausdorff dimension at most d − 5.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
