diff --git a/pytential/symbolic/primitives.py b/pytential/symbolic/primitives.py
index ea59b67652ef5cc1ecdce44fb95ce3c63bd70a49..7667fc0151ea4a62372ca874f374d94652bf01f4 100644
--- a/pytential/symbolic/primitives.py
+++ b/pytential/symbolic/primitives.py
@@ -1669,6 +1669,16 @@ def normal_derivative(ambient_dim, operand, dim=None, dofdesc=None):
             * d(operand))
 
 
+def normal_second_derivative(ambient_dim, operand, dim=None, dofdesc=None):
+    d = Derivative()
+    n = normal(ambient_dim, dim, dofdesc)
+    nabla = d.dnabla(ambient_dim)
+
+    return d.resolve(n.scalar_product(
+        n.scalar_product(nabla) * d(d.resolve(nabla * d(operand)))
+        ))
+
+
 def Sp(kernel, *args, **kwargs):
     dofdesc = kwargs.get("target")
     if "qbx_forced_limit" not in kwargs:
@@ -1702,9 +1712,9 @@ def Spp(kernel, *args, **kwargs):
     dim = kwargs.pop("dim", None)
 
     dofdesc = kwargs.get("target")
-    return normal_derivative(
+    return normal_second_derivative(
             ambient_dim,
-            Sp(kernel, *args, **kwargs),
+            S(kernel, *args, **kwargs),
             dim=dim, dofdesc=dofdesc)
 
 
diff --git a/test/test_symbolic.py b/test/test_symbolic.py
index 508ff2961b7b46a3a9b2eaa71530c1c8f4d58076..12145d692b12616037f54c20839fa579510071f5 100644
--- a/test/test_symbolic.py
+++ b/test/test_symbolic.py
@@ -201,6 +201,23 @@ def test_expr_pickling():
 # }}}
 
 
+# {{{ test basic layer potentials
+
+@pytest.mark.parametrize("lpot_class", [
+    sym.S, sym.Sp, sym.Spp, sym.D, sym.Dp
+    ])
+def test_layer_potential_construction(lpot_class, ambient_dim=2):
+    from sumpy.kernel import LaplaceKernel
+
+    kernel_sym = LaplaceKernel(ambient_dim)
+    density_sym = sym.var("sigma")
+    lpot_sym = lpot_class(kernel_sym, density_sym, qbx_forced_limit=None)
+
+    assert lpot_sym is not None
+
+# }}}
+
+
 @pytest.mark.parametrize(("name", "source_discr_stage", "target_granularity"), [
     ("default", None, None),
     ("default-explicit", sym.QBX_SOURCE_STAGE1, sym.GRANULARITY_NODE),